Bird shows remorse losing head (5)
I believe the answer is:
egret
'bird' is the definition.
(egret is a kind of bird)
'remorse losing head' is the wordplay.
'remorse' becomes 'regret' (I've seen this before).
'losing head' means to remove the first letter.
'regret' with its first letter removed is 'EGRET'.
'shows' acts as a link.
(Other definitions for egret that I've seen before include "Long-plumed heron" , "(Usually) white heron" , "White-plumed wader" , "Kind of heron with long white feathers" , "one with plume" .)