Magnificence of head of grey parrot (5)
I believe the answer is:
glory
'magnificence' is the definition.
(I've seen this before)
'head of grey parrot' is the wordplay.
'head of' suggests taking the first letters.
'parrot' becomes 'lory' (small parrot).
The initial letter of 'grey' is 'g'.
'g'+'lory'='GLORY'
'of' is the link.
(Other definitions for glory that I've seen before include "Splendour; high renown" , "The Power and the . . . . . (Graham Greene)" , "widespread praise" , "Lustre, prestige" , "Resplendent brightness" .)