Unbridled glee about a bird (5)
I believe the answer is:
eagle
'bird' is the definition.
(eagle is a type of bird)
'unbridled glee about a' is the wordplay.
'unbridled' is an anagram indicator (letters are unrestrained or unbridled).
'about' means one lot of letters goes inside another.
'glee' with letters rearranged gives 'egle'.
'egle' going around 'a' is 'EAGLE'.
(Other definitions for eagle that I've seen before include "Bird with hooked bill and long broad wings" , "Symbolic American bird" , "two strokes fewer?" , "High-flyer" , "Symbolic bird of the US" .)