Artist imprisoned by a bitter travelling judge (9)
I believe the answer is:
arbitrate
'judge' is the definition.
(to arbitrate is to judge or decide)
'artist imprisoned by a bitter travelling' is the wordplay.
'artist' becomes 'RA' (Royal Academician, member of Royal Academy of Arts).
'imprisoned by' means one lot of letters goes inside another.
'travelling' indicates anagramming the letters.
'a'+'bitter'='abitter'
'abitter' is an anagram of 'arbitte'.
'ra' inserted into 'arbitte' is 'ARBITRATE'.
(Other definitions for arbitrate that I've seen before include "Mediate" , "Decide" , "Act between disputing parties" , "judge" , "Help settle a dispute" .)