Arbitrary, right man being wrong about party (6)
I believe the answer is:
random
'arbitrary' is the definition.
(I've seen this before)
'right man being wrong about party' is the wordplay.
'right' becomes 'r' (common abbreviation).
'being wrong' indicates an anagram.
'about' indicates putting letters inside.
'party' becomes 'do' (do is a kind of party).
'man' is an anagram of 'anm'.
'anm' going around 'do' is 'andom'.
'r'+'andom'='RANDOM'
(Other definitions for random that I've seen before include "Haphazard, hit or miss" , "without conscious choice" , "Governed by chance" , "Without a particular aim, haphazard as choice may be" , "Disorganised" .)