Apostle's favourite perk is exposed (5)
I believe the answer is:
peter
'apostle's' is the definition.
(Peter is an example)
'favourite perk is exposed' is the wordplay.
'favourite' becomes 'pet' (synonyms).
'is exposed' indicates the central letters (outside letters removed).
The middle letters of 'perk' are 'er'.
'pet'+'er'='PETER'
(Other definitions for peter that I've seen before include "Boy's name (maybe blue)" , "Early Pope" , "Fellow < safe" , "till down under" , "prison cell" .)