In DS9: The Search (Part 2), the fake Admiral Alynna Nechayev refers to the groupings in the Alpha Quadrant as "Alliances":
NECHAYEV: They're already meeting with representatives from the Federation Council and a dozen other Alpha Quadrant alliances.
We're hoping to have a treaty signed within a matter of days, and we
have you to thank for it.
SISKO: Actually it's Lieutenant Dax and Chief O'Brien who deserve most of the credit.
The fake Romulan ambassador refers to them as "Great Powers" in the same episode:
BASHIR: I wasn't aware the Romulans had been excluded.
T'RUL: Every great power in the Alpha Quadrant has been invited to participate except for us.
BASHIR: There must be some mistake.
Odo also refers to them as such in DS9 : Inquisition:
BASHIR: I can't believe the Federation condones this kind of activity.
ODO: Personally, I find it hard to believe they wouldn't. Every other great power has a unit like Section thirty one. The Romulans
have the Tal Shiar, the Cardassians had the Obsidian Order.
BASHIR: But what does that say about us? When push comes to shove, are we willing to sacrifice our principles in order to
And so does Jaro in DS9: The Circle:
KIRA: How can you betray your own government?
JARO: Major, I don't have to tell you. I've heard your opinion of this government. Government. They can't even agree it is a government,
so they call it provisional. It's just another word for powerless. I
won't allow the Bajoran people to be powerless any more. We have been
doormats to the Cardassians and now the Federation. Any great power
that happens by. We will not be that again. We are a people who
brought art and architecture to countless planets. We don't deserve to
In DS9: Inter Arma Enim Silent Leges, Sloan simply refers to them as "powers":
SLOAN: To evaluate an ally. And a temporary ally at that. I say that because when the war is over, the following will happen in short
order. The Dominion will be forced back to the Gamma Quadrant, the
Cardassian Empire will be occupied, the Klingon Empire will spend the
next ten years recovering from the war and won't pose a serious threat
to anyone. That leaves two powers to vie for control of the
quadrant, the Federation and the Romulans.
as does Kirk in TOS: A Private Little War:
KIRK: Bones, do you remember the twentieth century brush wars on the Asian continent? Two giant powers involved, much like the Klingons
and ourselves. Neither side felt could pull out.
MCCOY: Yes, I remember. It went on bloody year after bloody year.
You may also wish to note that the (fully canon) Star Trek Encyclopedia refers to them throughout as the Alpha Quadrant powers, for example in this potted history of the Dominion War:
The war continued badly for the Alpha Quadrant powers until later in
that year when the Romulan Star Empire abrogated its nonaggression
treaty with the Dominion. A massive assault by Federation, Klingon,
and Romulan forces that captured the Chin'toka System from Cardassian
control represented a major turning point in the war. Nevertheless,
aided by Breen forces and sophisticated Breen weaponry, the Dominion
overwhelmed the Alpha Quadrant powers, despite the fact that a deadly
virus was infecting the Great Link. This biological weapon, a
genetically engineered disease developed by the Federation's Section
31, nearly wiped out the Founders. Despite an overwhelmingly powerful
military force, the Dominion began to lose ground when the Alpha
Quadrant powers developed the means to defend against Breen technology
It also tends to refers to them (individually) as "nations":
Klingon Neutral Zone : A no-man's-land between the United Federation of Planets and the Klingon Empire. Passage into the zone
by ships of either nation was forbidden by treaty. The Klingon Neutral Zone was abolished in 2293 by the Khitomer Accords
Romulan Star Empire. : The formal name of the Romulan nation. An enigmatic offshoot of the Vulcan civilization, now residing on
planets Romulus and Remus