Bishop presses son to become freeman of borough (7)
I believe the answer is:
burgess
'freeman of borough' is the definition.
(I've seen this before)
'bishop presses son' is the wordplay.
'bishop' becomes 'B' (chess abbreviation).
'presses' becomes 'urges' ('urge' can be a synonym of 'press').
'son' becomes 's' (genealogical abbreviation for son).
'b'+'urges'+'s'='BURGESS'
'to become' is the link.
(Other definitions for burgess that I've seen before include "Citizen of a borough" , "Guy who spied" , "Former MP for a borough or university" , "English novelist, 1917-93 - Soviet spy, 1911-63" , "Old representative" .)