He's dead keen (5)
I believe the answer is:
david
'he's' is the definition.
'dead keen' is the wordplay.
'dead' becomes 'd'.
'keen' becomes 'avid' (I've seen this in other clues).
'd'+'avid'='DAVID'
(Other definitions for david that I've seen before include "friend of Jonathan's?" , "Israeli king" , "Hebrew king" , "Camp" , "- Copperfield (Dickens)" .)