Relationship made a fellow even-handed (6)
I believe the answer is:
affair
'relationship' is the definition.
(I know that affair is a type of sexual relationship)
'a fellow even-handed' is the wordplay.
'fellow' becomes 'f' (abbreviation - of a society etc.).
'even-handed' becomes 'fair' (I've seen this before).
'a'+'f'+'fair'='AFFAIR'
'made' acts as a link.
(Other definitions for affair that I've seen before include "Former Belgian coin" , "Clandestine romance" , "Event; fling" , "Concern,matter" , "Liaison or intrigue" .)