Cover over a bird (5)
I believe the answer is:
capon
'a bird' is the definition.
(capon is a kind of bird)
'cover over' is the wordplay.
'cover' becomes 'cap' (capping is a kind of covering).
'over' becomes 'on' (physically on top of).
'cap'+'on'='CAPON'
(Other definitions for capon that I've seen before include "Emasculated fowl" , "Castrated cock fowl" , "fowl fattened for pot" , "one fattened specially" , "Castrated bird" .)