Nonconformist and bishop in dance (5)
I believe the answer is:
rebel
'nonconformist' is the definition.
(rebel is a kind of nonconformist)
'bishop in dance' is the wordplay.
'bishop' becomes 'b' (abbreviation used in chess).
'in' indicates putting letters inside.
'dance' becomes 'reel' (reel is a kind of dance).
'b' put inside 'reel' is 'REBEL'.
'and' is the link.
(Other definitions for rebel that I've seen before include "Rise up (without a cause?)" , "Unconventional type" , "One who rises up" , "Disobey" , "Flouter of authority" .)