Unusually eager to correspond (5)
I believe the answer is:
agree
'correspond' is the definition.
(agreeing is a kind of corresponding)
'unusually eager' is the wordplay.
'unusually' indicates anagramming the letters.
'eager' with letters rearranged gives 'AGREE'.
'to' is the link.
(Other definitions for agree that I've seen before include "See eye to eye" , "Be of one mind" , "Square" , "Concur, acquiesce" , "Think alike" .)