One with a degree argued at random (8)
I believe the answer is:
graduate
'one with a degree' is the definition.
(I've seen this before)
'argued at random' is the wordplay.
'random' is an anagram indicator.
'argued'+'at'='arguedat'
'arguedat' is an anagram of 'GRADUATE'.
(Other definitions for graduate that I've seen before include "progress" , "University alumnus" , "Holder of university degree" , "Move to the next stage" , "Person who has gained university degree" .)