Glutton takes an age to finish a bird (6)
I believe the answer is:
pigeon
'bird' is the definition.
(type of bird)
'glutton takes an age' is the wordplay.
'glutton' becomes 'pig' (I've seen this before).
'takes' means one lot of letters go next to another.
'an age' becomes 'eon' (eon is a kind of age).
'pig'+'eon'='PIGEON'
'to finish a' acts as a link.
This may not be right. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for pigeon that I've seen before include "Common town bird" , "Trafalgar Square bird?" , "Dupe" , "Bird of towns and woods" , "Town and woodland bird" .)