In the Star Trek The Next Generation episode Lonely Among Us there are two species being transported on board from warring races. There is a lot of animosity between the two races throughout the entire episode, and at the end there is a strong implication that the Anticans had killed and were about to eat one of the Selay delegates.
First the implication of them having eaten an "interesting animal":
TASHA: I must ask where you were during this vessel's Earth hours of eighteen hundred last night and zero seven hundred this morning.
TASHA: Sir, we're talking about hours here.
ANTICAN: It was a large meal, Lieutenant Yar. And a very interesting animal.
At the end of the episode Tasha implies that the Anticans are about to make a meal of another delegate:
TASHA: It's good to see you, sir. The problem is that one of the cooks has just been asked to broil reptile for the Anticans, and it looks like the Selay delegate.
(Picard in brilliant fashion turns this problem over to Riker in a jovial manner of course).
While the actual act of eating isn't shown, and in fact there is only the implication and not a direct statement of fact, it is obvious that Tasha believes that it is more than likely that one of the Anticans could eat one of the Selays. Enough so to bring up the fact to her captain. So whether they did eat them or not in this case, the implication answers the question about whether it happens with a resounding; yes.