Grey ale drunk with enthusiasm (7)
I believe the answer is:
eagerly
'with enthusiasm' is the definition.
(I've seen this in another clue)
'grey ale drunk' is the wordplay.
'drunk' indicates an anagram.
'grey'+'ale'='greyale'
'greyale' anagrammed gives 'EAGERLY'.
(Other definitions for eagerly that I've seen before include "Fervently" , "Enthusiastically" , "Keenly" , "With keen anticipation" , "In a keen manner" .)