Feel sorry for losing head with bird (5)
I believe the answer is:
egret
'bird' is the definition.
(egret is a kind of bird)
'feel sorry for losing head' is the wordplay.
'feel sorry for' becomes 'regret' (I've seen this before).
'losing head' means to remove the first letter.
'regret' with its first letter taken off is 'EGRET'.
'with' acts as a link.
(Other definitions for egret that I've seen before include "Wader with white plumage" , "(Usually) white heron" , "Wading bird like a heron" , "Mainly white heron" , "young bird" .)