Fellow's cottage finally becoming minister's residence (5)
I believe the answer is:
manse
'minister's residence' is the definition.
(house for a religious minister)
'fellow's cottage finally' is the wordplay.
'fellow's' becomes 'mans' (man's).
'finally' indicates one should take the final letters.
The last letter of 'cottage' is 'e'.
'mans'+'e'='MANSE'
'becoming' acts as a link.
(Other definitions for manse that I've seen before include "Ecclesiastical residence" , "Pile of rector'" , "Religious home" , "Names (anag.)" , "Scottish minister's residence" .)