Part of a church’s fortune, land primarily (7)
I believe the answer is:
chancel
'part of a church's' is the definition.
('chancel' is part of 'church')
'fortune land primarily' is the wordplay.
'fortune' becomes 'chance' (synonyms).
'primarily' indicates taking the first letters.
The first letter of 'land' is 'l'.
'chance'+'l'='CHANCEL'
(Other definitions for chancel that I've seen before include "choir and clergy's area" , "Where to see choir" , "where choir sits" , "what's behind the screen" , "where sanctuary may be found" .)