Greek character in row is less sober (7)
I believe the answer is:
tipsier
'less sober' is the definition.
(I've seen this before)
'greek character in row' is the wordplay.
'greek character' becomes 'psi' (letter from the Greek alphabet).
'in' is an insertion indicator.
'row' becomes 'tier' (a tier is a row of things).
'psi' going into 'tier' is 'TIPSIER'.
'is' acts as a link.
(Other definitions for tipsier that I've seen before include "Less sober" , "Happier" .)