Remorse beheaded a bird (5)
I believe the answer is:
egret
'a bird' is the definition.
(egret is a kind of bird)
'remorse beheaded' is the wordplay.
'remorse' becomes 'regret' (remorse is a feeling of regret).
'beheaded' means to remove the first letter (the head of the word is removed).
'regret' with its initial letter taken away is 'EGRET'.
(Other definitions for egret that I've seen before include "Wader with white plumage" , "White-feathered wading bird" , "Kind of heron with long white feathers" , "Kind of white heron - greet it" , "flier" .)