Second minor argument is awkward (5)
I believe the answer is:
stiff
'awkward' is the definition.
(I've seen this before)
'second minor argument' is the wordplay.
'second' becomes 's' (common abbreviation).
'minor argument' becomes 'tiff' (I've seen this before).
's'+'tiff'='STIFF'
'is' acts as a link.
(Other definitions for stiff that I've seen before include "tough" , "Starched, rigid" , "cheat" , "Severe - conventional - dead body" , "Not giving" .)