Decide on a right piece to assess (9)
I believe the answer is:
arbitrate
'decide' is the definition.
(I've seen this before)
'on a right piece to assess' is the wordplay.
'on' is a charade indicator (letters next to each other).
'right' becomes 'r' (common abbreviation).
'piece' becomes 'bit' (bit is a kind of piece**).
'to assess' becomes 'rate' (rating is a kind of assessing).
'a' next to 'r' is 'ar'.
'ar'+'bit'+'rate'='ARBITRATE'
(Other definitions for arbitrate that I've seen before include "Act between disputing parties" , "Mediate" , "Decide" , "judge" , "Help settle a dispute" .)