Terribly eager to be consistent (5)
I believe the answer is:
agree
'be consistent' is the definition.
(I've seen this in another clue)
'terribly eager' is the wordplay.
'terribly' indicates anagramming the letters.
'eager' anagrammed gives 'AGREE'.
'to' acts as a link.
(Other definitions for agree that I've seen before include "Shake on it" , "Hold the same view" , "Think alike" , "See eye to eye" , "Give consent" .)