The United Federation of Planets, has over the years, had great rivals like the Klingons, Romulans, the Cardassians and the Borg.
With relative peace with the Klingons, the Cardassians devastated by the Dominion Wars, the Romulans now without their home planet and the Borg affected by a neurolytic pathogen unleashed by Janway, which space faring civilzation can take on the mantle of being the Federation's next nemesis.
The Breen ? Some other new race perhaps ?
One problem with your question is logic.
Political and military rivals and enemies of a state, such as for example the USA, are not ethnic groups or nationalities like the Russians or the Iranians, for example, but states, such as the USSR, the Russian Federation, China, Iran, Germany during Nazi rule, for example.
So rivals of the Untied Federation of Planets would be other unitary states or Federations, such as the Klingon Empire, the Romulan Empire, the Cardassian Union, the Borg Collective, the Dominion, etc. Not species like the Klingons, or the Romulans (who are merely a group of Vulcans and not a species themselves), or the Cardassians, or the Borg, or the Changlings.
If the United Federation of Planets rules one hundred highly advanced planets with populations in the billions, a state which would be a plausible rival for the Federation would also have to rule approximately one hundred approximately as highly advanced planets with populations in the billions.
If the United Federation of Planets rules one thousand highly advanced planets with populations in the billions, a state which would be a plausible rival for the Federation would also have to rule approximately one thousand approximately as highly advanced planets with populations in the billions.
If the United Federation of Planets rules ten thousand highly advanced planets with populations in the billions, a state which would be a plausible rival for the Federation would also have to rule approximately ten thousand approximately as highly advanced planets with populations in the billions.
If the United Federation of Planets rules one hundred thousand highly advanced planets with populations in the billions, a state which would be a plausible rival for the Federation would also have to rule approximately one hundred thousand approximately as highly advanced planets with populations in the billions.
If the United Federation of Planets rules one million highly advanced planets with populations in the billions, a state which would be a plausible rival for the Federation would also have to rule approximately one million approximately as highly advanced planets with populations in the billions.
And so on and so on. The larger and more powerful the Federation is, the larger and more powerful a state would have to be to function as a plausible rival for the Federation.
I suppose that it would be possible for a state that ruled one hundred highly advanced planets with populations in the billions on each planet to be populated only by members of a since species. In analogy with the term "nation state"", I call a single species state which interacts with other states in interstellar space a "species state". And if a species evolved on one home planet and colonized 99 other planets in other star systems those colony worlds should eventually build up their infrastructure and population until each colony world had as large a population and as much industry as the home world. So a species state with one hundred highly advanced planets with populations in the billions on each planet would be possible in real life, where nobody knows what percentage of habitable planets have native intelligent lifeforms. It is possible that only one habitable planet out of a thousand, or one out of a million, or one out of a billion,etc., has native intelligent life forms in real life.
But planets with native intelligent life are seen to be very common in
Star Trek. If a species expanded from their home star to one hundred other star systems with habitable planets they could colonies, and formed a species state ruling over those one hundred star systems, they would probably have to pass over a number of star systems with inhabited planets and leave those systems as enclaves in their space, if inhabited planets are as common as they are in
Star Trek.
And that would be even more so if the species state ruled two hundred planets, three hundred planets, four hundred planets, a thousand planets, or ten thousand planets, etc., etc. The larger an interstellar species state is, the more likely it will be to resemble a wheel of Swiss cheese, with many spherical holes where there are enclave systems with native intelligent life that aren't ruled by the species state.
So how much larger could an interstellar government get? As you remember, I discussed an interstellar government with one hundred planets, or with one thousand planets, or with ten thousand planets, or with one hundred thousand planets, or with one million planets. Surely a interstellar government couldn't rule more than one million highly advanced planets.
Our Milky Way galaxy has least about one hundred billion star systems in it.
It is estimated to contain 100–400 billion
stars[26][27] and more than 100 billion
planets
https://en.wikipedia.org/wiki/Milky_Way
Both
gravitational microlensing and planetary transit observations indicate that there may be at least as many planets bound to stars as there are stars in the Milky Way,
[28][75] and microlensing measurements indicate that there are more
rogue planets not bound to host stars than there are stars.
[76][77] The Milky Way contains at least one planet per star, resulting in 100–400 billion planets, according to a January 2013 study of the five-planet star system
Kepler-32 with the
Kepler space observatory.
[29] A different January 2013 analysis of Kepler data estimated that at least 17 billion
Earth-sized exoplanets reside in the Milky Way.
[78] On November 4, 2013, astronomers reported, based on
Kepler space mission data, that there could be as many as 40 billion Earth-sized
planets orbiting in the
habitable zones of
Sun-like stars and
red dwarfs within the Milky Way.
[79][80][81] 11 billion of these estimated planets may be orbiting Sun-like stars.
[82]
https://en.wikipedia.org/wiki/Milky_Way
So if there might be billions of habitable planets in the Milky Way galaxy, there could be room for thousands of interstellar states that ruled one million habitable planets each. So if faster than light travel is possible, an interstellar state that eventually grows to rule much more than one million habitable planets might still rule much less than one percent of the Milky Way galaxy. And that is in the real Milky Way galaxy. But since habitable planets are so very much more common in the Milky Way Galaxy in
Star Trek, interstellar states that rule a million habitable planets would rule much smaller fractions of a percent of the total Milky Way galaxy in
Star Trek.
And so I can't help expecting that any important state in
Star Trek is likely to be a federation or empire ruling many planets with many different intelligent species instead of a species state ruling only planets inhabited by one single species.
.
