Entertain a creative influence (5)
I believe the answer is:
amuse
'entertain' is the definition.
(amusing is a kind of entertaining)
'a creative influence' is the wordplay.
'creative influence' becomes 'muse' (I've seen this in another clue).
'a'+'muse'='AMUSE'
(Other definitions for amuse that I've seen before include "Enliven" , "Reflect" , "Keep someone entertained" , "Pleasantly occupy" , "Recreate" .)