Somewhere down the line after this episode and The Undiscovered Country relations between the Federation and the Romulan Empire must have thawed a little to allow a Romulan into the offices of the Federation President while they planned war with the Klingons who at one time were the allies of the Romulans!

JB
I wrote a long reply to this the other day but I lost it.
Short Comment:
According to my chronological calculations, there should have been a big war with the Klingons not long before
Star Trek VI: The Undiscovered Country, and i think that there is good reason to believe that Ambassador Nunclus was responsible for saving the Federadtion by arranging a military alliance with the Romulans to defeat the Klingons. This he was influential enough to be invited to secret meetings.
Long Comment:
According to the official, but not necessarily canon or correct chronology, the TNG episodes "The Emissary" and "Unification Part 1" & "Unification part 2" happen in AD 2365 and AD 2368 respectively.
In "Unification Part 1":
PICARD: Is there anyone on Romulus he might know, or choose to contact?
SAREK: Pardek?
PICARD: Who is Pardek?
SAREK: It could be Pardek.
PICARD: Who is Pardek?
SAREK: He is a Romulan Senator. Spock has maintained a relationship with him over the years. I don't know how they met. At the Khitomer Conference, I'd imagine.
PICARD: Pardek represented Romulus?
SAREK: Yes, I'm sure he did. In fact, I recall Spock coming to me with optimism about a continuing dialogue with the Romulans. I told him it was illogical to maintain such an expectation. Spock was always so impressionable. This Romulan, Pardek, had no support at home. Of course, in the end I was proven correct. I gave Spock the benefit of experience, of logic. He never listened. Never listened.
So sArek believes that Spock first met Pardek at the Khitomer Conference.
In "Unification Part 2":
PARDEK: Spock, we've been friends for eighty years.
Assuming that Pardek meant 75 to 85 Earth years, Pardek should have become friends with Spock about AD 2283 to 2293 if the official chronology is correct, and they presumably became friends at the Khitomer Conference during and after
Star Trek VI: The Undiscovered Country, which should thus have been sometime in the period of 2283 to 2293.
In "The Emissary":
K'EHLEYR: Haven't changed a bit. Well, I missed you, too. Two days ago, Starbase Three Three Six received an automated transmission from a Klingon ship, the T'Ong. That ship was sent out over seventy five years ago.
RIKER: When the Federation and the Klingon Empire were still at war.
K'EHLEYR: The message was directed to the Klingon High Command. It said only that the ship was returning home and was about to reach its awakening point.
PICARD: Which suggests that the crew had been in cryogenic sleep for that long journey.
K'EHLEYR: Exactly.
RIKER: And when this crew is revived?
K'EHLEYR: We'll have a ship full of Klingons who think the war is still going on.
PICARD: So our task is to find the ship, and tell the Klingons they're no longer at war.
RIKER: Why us? Wouldn't a Klingon ship be a better choice?
K'EHLEYR: A Klingon ship, the P'rang, is on its way, but it's two days behind us. That may be too late.
TROI: Why too late?
RIKER: When the T'Ong crew awakens it will be within striking range of several Federation outposts.
DATA: There are thirteen colonies with minimal defences in that sector.
K'EHLEYR: Nice, ripe targets for a Klingon warship.
TROI: And you believe you can convince these Klingons that the humans are now their allies?
K'EHLEYR: No, not a chance. If you ask me, talking will be a waste of time. Klingons of that era were raised to despise humans. We'll try diplomacy. But I promise you it won't work. And then you'll have to destroy them
So if "over 75 years" is 75 to 80 years, or maybe 75 to 100 years, the possible date when the T"Ong left on its mission would have been between AD 2285 and 2290, or maybe between AD 2265 and 2290 - if the official chronology is correct.
Thus the T'Ong could have been sent out either before, during, or after
Star Trek VI: The Undiscovered Country, which should have been sometime in the period of 2283 to 2293.
The way they expect that the Klingons will attack any Federation outposts they find seems to prove that when the T'Ong was sent there was an all out war between the Federation and the Klingons, and that the Klingons in that era expected that the war would last until the Federation was totally fe defeated and conquered bythe klings, even if it took many decades. the attitude of the Klingons on the T'Ong shows that they came from a era of war with the Federation, not rivalry or cold war but all out war. And they say three times that the when the Klingons left there was a war on.
So the attitude in "The Emissary" is that when the T'Ong was sen ton its mission and before peace was made the Klingons were at war with the Federation, and perhaps had been almost constantly at war with the Federation for a long time, perhaps for many decades or centuries, so that the crew of the T'Ong would not imagine peace with an unconquered Federation.
If the T'Ong was sent on its mission after the events in
Star Trek VI: The Undiscovered Country that would show that all that the heroes endured in the cause of peace in that movie was for nothing and war resumed soon after the movie, and someone else, like Riva in "Loud as a Whisper" was responsible for making peace between the Federation and the Klingons. And certainly fans of the TOS crew would not think that was a good idea! .
Since the Klingon chancellor Gorkon was already considering making peace with the Federation at the beginning of
Star Trek VI: The Undiscovered Country, which probably didn't last a very long time anyway, it is unlikely that the T'Ong was sent on its mission during
Star Trek VI: The Undiscovered Country.
And this is when the Excelsior encounters the shock wave from the explosion of Praxis at the beginning of
Star Trek VI: The Undiscovered Country:
VALTANE: Negative, sir. The subspace shockwave originated at bearing three two three, mark seven five. Location. It's Praxis, sir. It's a Klingon moon.
SULU: Praxis is their key energy production facility. ...Send to Klingon High Command. 'This is Excelsior, a Federation starship. We have monitored a large explosion in your sector. Do you require assistance?'
RAND: Aye sir.
SULU: Mister Valtane, any more data?
VALTANE: Yes sir. I have confirmed the location of Praxis, sir, but...
SULU: What is it?
VALTANE: I cannot confirm the existence of Praxis.
SULU: On screen! ...Magnify!
COMPUTER VOICE: Computer enhancement.
SULU: Praxis?
VALTANE: What's left of it, sir.
RAND: Captain, I'm getting a message from Praxis.
SULU: Let's have it.
KERLA (on viewscreen): This is Brigadier Kerla, speaking for the High Command. There has been an incident on Praxis. However everything is under control. We have no need for assistance. Obey treaty stipulations and remain outside the Neutral Zone. This transmission ends now.
So Sulu offers assistance during the disaster to the Klingons, which would be a little unusual during a war with the Klingons, and the Klingon Kerla tells Sulu to obey treaty stipulations and remain outside the Neutral Zone. Taht seems to pretty much prove there is a peace treaty with the Klingons at the beginning of
Star Trek VI: The Undiscovered Country.
So that leaves the period before
Star Trek VI: The Undiscovered Country for the T'Ong being sent on its mysterious long term mission.
So that leaves a period of possibly as much as 28 years between 265? and 2290? and
Star Trek VI: The Undiscovered Country sometime between 2283? and 2293? when the T'Ong might have left.
And from the way that the characters talk in "The Emissary",and from what Spock says in
Star Trek VI: The Undiscovered Country about:
SPOCK: The dismantling of our space stations and starbases along the Neutral Zone, an end to almost seventy years of unremitting hostility, which the Klingons can no longer afford.
There could have been almost 70 years before
Star Trek VI: The Undiscovered Country of almost constant warfare between the Klingons and the Federation. Possibly there was one year of short lived peace for every five years or ten years of warfare, for example, during that almost 70 year period..
The inconclusive Battle of Donatu Five 23 years before "The Trouble With Tribbles" could have been a vast battle in a long and bloody war with the Klingons, or maybe it was just a minor frontier skirmish during a time of peace with the Klingons.
There is peace with the Klingons for most of TOS and TAS.
In "Errand of Mercy":
KIRK: Good. (puts it into a decoder) We both guessed right. Negotiations with the Klingon Empire are on the verge of breaking down. Starfleet Command anticipates a surprise attack. We are to proceed to Organia and take whatever steps are necessary to prevent the Klingons from using it as a base.
And:
UHURA: Automatic all-points relay from Starfleet Command, Captain, code one.
KIRK: Well, there it is. War. We didn't want it, but we've got it.
Fortunately the war seems to last just a matter of days before a peace is imposed.
In "Friday's Child":
KRAS: I am unaware of any state of war between our peoples, Captain.
MCCOY: Jim!
KRAS: Or is it your policy to kill Klingons on sight?
KIRK: He was young, and inexperienced.
MCCOY: Does Maab know that the Klingons are our sworn enemies by their own words?
In "The Trouble With Tribbles":
CHEKOV: Under terms of the Organian Peace Treaty, one side or the other must prove it can develop the planet most efficiently.
KOLOTH: Let me assure you that my intentions are peaceful. As I've already told Mister Lurry, the purpose of my presence is to invoke shore leave rights.
KIRK: Shore leave?
KOLOTH: Captain, we Klingons are not as luxury-minded as you Earthers. We do not equip our ships with, how shall I say it, non-essentials. (makes an hour-glass gesture with his hands)
KORAX: We have been in space for five months. What we choose as recreation is our own business.
KOLOTH: I might also add that under terms of the Organian Peace Treaty, you cannot refuse us.
KIRK: Yes, well, I don't make those decisions. Mister Lurry is in charge of those matters.
LURRY: Captain, may I speak to you a minute? (takes him aside) Look, I don't want them here, but I don't have the authority to refuse.
KIRK: Well, I have the authority to act, and I'm going to use it. My dear Captain Koloth, you may indeed bring your men down on shore leave, but only twelve at a time. And I assure you, for every man you bring down here, I shall have one security guard. There will be no trouble.
KOLOTH: Captain Kirk, there's been no formal declaration of hostilities between our two respective governments. So, naturally, our relationship will be a peaceful one.
In "A Private Little War":
KIRK: So, they've broken the treaty.
SCOTT: Not necessarily, Captain. They have as much right to scientific missions here as we have.
KIRK: Research is not the Klingon way.
SCOTT: True, but since this is a hands-off planet, how are you going to prove they're doing otherwise?
KIRK: When I left there thirteen years ago, those villagers had barely learned to forge iron. Spock was shot with a flintlock. How many centuries between those two developments?
In "The Day of the Dove":
(The Klingons arrive, and their leader hits Kirk with his disruptor, knocking him down.)
KANG: You attacked my ship! Four hundred of my crew dead. Kirk, my ship is disabled. I claim yours. You are now prisoners of the Klingon Empire against which you have committed a wanton act of war!
(And a weird swirl of light hangs in the air a little way away. The Federation landing party are disarmed.)
However, there is little evidence for how much war and how much peace there was in the period between TOS and
Star Trek VI: The Undiscovered Country.
If stardate units have a fixed relationship with the passage of time on planets, and if only the last four digits of stardates with more digits are used in the era of TOS there could be 11,466.5 stardates instead of only 1,466.5 stardates between "All Our Yesterdays" at 5943.7 and
Star Trek: The Motion Picture at 7410.2, ans 10,720.1 stardates instead of only 720.1 between
Star Trek: The Motion Picture at 7410.2 and
Star Trek II: The Wrath of Khan at 8130.3.
The movies between
Star Trek II: The Wrath of Khan at 8130.3.and
Star Trek V: The Final Frontier at 8454.1 all seem to happen within a few months of fictional time, certainly less than one year, so 323.8 star dates between them seem like enough.
And there could be 11,067.5 stardates instead of of only 1,067.5 between
Star Trek V: The Final Frontier at 8454.1 and
Star Trek VI: The Undiscovered Country at 9521.6.
So the total number of stardates between "All Our Yesterdays" at 5943.7 and
Star Trek VI: The Undiscovered Country at 9521.6 could be tween 3,577.9 and 33,577.9. Assuming that there are two to four stardates per Earth day, there could be 2.448 to 4.897 years in 3.577.9 stardates and 22.982 to 45.965 years in 33,577.9 stardates.
Although it is hard to be certain, there seems to be a condition of peace between the Federation and the Klingons in most or all of the TOS movies.
But Starfleet seems highly militarized in
Star Trek II: The Wrath of Khan and its sequels. Therefore, one could surmise that there was about a decade of war with the Klingons between
Star Trek: The Motion Picture and
Star Trek II: The Wrath of Khan, followed by a year or two of peace that included the era of the movies from
Star Trek II: The Wrath of Khan to
Star Trek V: The Final Frontier, followed by another long war with the Klingons beginning soon after
Star Trek V: The Final Frontier and continuing to shortly before
Star Trek VI: The Undiscovered Country when another period of peace began. But that period of peace would have been a short one if Praxis had not exploded, because the Klingons were still committed to conquering the Federation.
And we can imagine that Kirk was a great tactician and strategist in those hypothetical long and bloody Klingon wars.
And to finally get to the point of answering the comment, possibly the Klingons would have defeated the Federation in the second of those wars if Ambasador Nunclus had not negotiated an alliance between the Federation and the Romulans and brought a lot of Romulan military help to defeat the Klingons,thus preventing the Klingosn from possibly becoming powerful enough to to conquer theRomulans. Thus Nunclus would have been highly respected and influential, and it would be more likely for the President of the Federation to invite Nunclus to a meeting discussing top secret rescue operations.