Bird taking top off for creep (4)
I believe the answer is:
inch
'creep' is the definition.
(I've seen this before)
'bird taking top off' is the wordplay.
'bird' becomes 'finch' (finch is a kind of bird).
'taking top off' means to remove the first letter.
'finch' with its first letter taken off is 'INCH'.
'for' acts as a link.
(Other definitions for inch that I've seen before include "One-twelfth of a foot" , "... or not so long < , Celtic island" , "One point 63380 th of a mile" , "Crawl; imperial measurement" , "Advance slowly" .)