Nonconformist putting bishop into spin (5)
I believe the answer is:
rebel
'nonconformist' is the definition.
(rebel is a kind of nonconformist)
'bishop into spin' is the wordplay.
'bishop' becomes 'b' (abbreviation used in chess).
'into' indicates putting letters inside.
'spin' becomes 'reel' ('reel' can be a synonym of 'spin').
'b' going inside 'reel' is 'REBEL'.
'putting' acts as a link.
(Other definitions for rebel that I've seen before include "One refusing to conform" , "Insurgent, renegade" , "James Dean was one without a cause" , "Rise in armed opposition" , "Mutineer or dissenter" .)