Feel sorry for overlooking first river bird (5)
I believe the answer is:
egret
'bird' is the definition.
(egret is a kind of bird)
'feel sorry for overlooking first river' is the wordplay.
'feel sorry for' becomes 'regret' (I've seen this before).
'overlooking' indicates named letters should be taken away.
'first river' becomes 'r' (1st letter of 'river').
'regret' with 'r' taken away is 'EGRET'.
(Other definitions for egret that I've seen before include "One wading" , "white fish eater" , "Type of heron" , "Bird eating fish" , "Mainly white heron" .)