Isn't this a bit like referring to the United Federation of Planets as the Federal Federation?
I am redundently annoyed by the many redundent claims that the phrase "Klingon Imperial Empire' is redundent, so I will redundently refute that claim several times over.
One) Isn't it common in English for words to have more than one meaning, and for more than one word to have the same meaning.
So it is perfectly possible that :Imperial" is a translation of a Klingon adjective that is completely unrelated to the Klingon noun which is trnslated as "empire" in "kingon Imperial Empire"..
Two) There were a number of separate Boer or Afrikaner states and republics in 19th century Africa - usually 2 or more at the same time. This is an example of a nationality or an ethnic group having more than one sovereign state at the same time.
https://en.wikipedia.org/wiki/Boer_Republics
How many separate and independent soverign Greek city states were there in Classical Greece and around the Mediterranean? Tens. Possibly more than a hundred. So that is an example of an ethnic group or nationality having tens or even more than a hundred separate soverign states.
There grew to be over 1,000 city-states in ancient Greece, but the main poleis were Athína (Athens), Spárti (Sparta), Kórinthos (Corinth), Thíva (Thebes), Siracusa (Syracuse), Égina (Aegina), Ródos (Rhodes), Árgos, Erétria, and Elis.
https://www.nationalgeographic.org/encyclopedia/greek-city-states/
https://en.wikipedia.org/wiki/List_of_ancient_Greek_cities
In the present time there is North and South Korea, the Republic of China and the People's Republic of China, the former South and North Vietnam, and the former German Democratic Republic and Federal Republic of Germany. All showing that a nationality or ethnic group can have more than one soverign state at the same time.
So if the Klingons are analogous to a nationality or an ethic group they can have more than one sovereign state.
If Klingons are defined as a species of intelligent beings, scientists do not agree on more than one such species existing at the present time with political organizations which can be studied. I note that I have seen a historical article claiming that the total number of separate independent sovereign politcal entities among the human species has declined from about tens or hundreds of thousands several thosuand years ago to about 50 at one point in the 20th century and then increased to about 200 today. I believe the article calculated that there should be only one sovereign human government by about AD 4000 or so.
So I suspect that various splinter groups of Klingons constantly found their own states which last for longer or shorter times. I think that Gorkon's Klingon realm was probably not the only Klingon realm in his time, though probably by far the most important, and that a lot of Klingon groups broke away from Gorkon's realm and founded their own realms after the events in
Star Trek: The Undiscovered Country.
So possibly there are a bunch of Klingon realms in the era of TNG with names like Klingon Imperial Republic, Klingon Royal Republic, Klingon Republican Republic, Klingon Imperial Kingdom, Klingon Royal Kingdom, Klingon Republican Kingdom, Klingon Imperial Empire, Klingon Royal Empire, and Klingon Republican Empire, to say nothing of the Klingon realms with long and complicted names.
Three) What is the best example of an emipire in Earth history? There could be many possible examples, but one which many would choose would be the Roman Empire.
The first emperor seized absolute power with his army, but pretened to be merely the mos tinfluential senator, and had the Senate and people grant him a number of Republican offices and powers to provide Repuliban justification for his authority. Thus Roman emperors were known by a number of different titels, such as:
Princeps,
Caesar,
Imperator,
Augustus,
Pontifex Maximus,
Dominus, etc.
Often a heir to the throne or a junior emperor would be an
Imperator Caesar, while a senior emperor would be an
Imperator Caesar Augustus. This sort of implies that the word .
Augustus, or the three word phrase .
Imperator Caesar Augustus, should be considered to be the imperial title.
In the Greek speaking east of the Roman Empire, hte imperial titles were often transliterated into the Greek alphabet. But they were also often translated into Greek words which were not very accurate translations.
The Emperor was often called
Basileus, which originally meant the king of a tiny Greek city state, but was then used in the sense of "King of the World", and very roughly equivalent to Emperor.
And the Latin tittle of
imperator was translated, not very accurately, into Greek as
autokrator.
By about AD 900 the title of the senior eastern emperor was usually
Basileus kai Autokrator ton Rhomaion, which is usually translated as "emperor and Autocrat of the Romans". A more literal translation would be "King and Empreror of the Romans".
Basileus kai Autokrator could be considere a three word phrase emeaning emperor, making the title "Emperor of the Romans", or it could be translated as "Emperor and Emperor of the Romans".
.
Charlemagne,the first Holy Roman Emperor, use a long title:
In his official charters, Charles preferred the style
Karolus serenissimus Augustus a Deo coronatus magnus pacificus imperator Romanum gubernans imperium[109] ("Charles, most serene Augustus crowned by God, the great, peaceful emperor ruling the Roman empire") to the more direct
Imperator Romanorum ("Emperor of the Romans").
https://en.wikipedia.org/wiki/Charlemagne#Imperial_title
Imperator augustus was the title of the early Holy Roman Emperors.
Imperator augustus could be interpreted as a two word phrase meaning "emperor"..Or it could be interpreted as "emperor emperor".
By about 1200 the person elected future emperor used the title of
Rex Romanourm et semper Augustus, which seems to translate as "King of the Romans and always Emperor". When and if he was crowned emperor in Rome by the pope, he used the title of
Rex Romanourm et semper Augustuss, "Emperor of the Romans and always Emperor".
I have seen
semper Augustuss translated into English as "always august". And I suspect that was done by people who never suspected that that there could possibly have been redundently imperial imperius Roman Emperors.
Four) So I get a little annoyed when peopel write that "Klingon imperial Empire" is redundent.
What I don't like is the order of words in the phrase. It seems much more natural in the English language to write names like "Royal Klingon Republic" and "Demoratic Klingon Kingdom" and "Imperial Klingon Empire"
So I wonder if the "Klinngon Imperial Empire" is named to show that it is different - being ruled by Klingons - from some other "imperial empires" which are known, such as the Romulan Imperial Empire, the Breen Imperial Empire, the Denubian imperial empire, etc.