Regret gripping Left facing Republican leader (5)
I believe the answer is:
ruler
'leader' is the definition.
(I know that ruler is a type of leader)
'regret gripping left facing republican' is the wordplay.
'regret' becomes 'rue' (to rue something is to regret it).
'gripping' is an insertion indicator (inserted letters are gripped).
'left' becomes 'l' (common abbreviation).
'facing' is a charade indicator (letters next to each other).
'republican' becomes 'R' (abbreviation in US politics).
'rue' going around 'l' is 'rule'.
'rule'+'r'='RULER'
(Other definitions for ruler that I've seen before include "Potentate" , "Graduated straight-edge" , "Royal" , "Measuring rod; governor" , "Man in charge" .)