Bird heading off remorse (5)
I believe the answer is:
egret
'bird' is the definition.
(egret is a kind of bird)
'heading off remorse' is the wordplay.
'heading off' means to remove the first letter.
'remorse' becomes 'regret' (remorse is a feeling of regret).
'regret' with its initial letter removed is 'EGRET'.
(Other definitions for egret that I've seen before include "White, plumed waterbird" , "Type of forty eight Ac" , "Heron-like wader" , "Bird eating fish" , "Greet (anag) -- wading bird" .)