Old left-winger is in grip of drink after upholding the very thing (7)

'old left-winger' is the definition.
(supporter of Josip Tito of Yugoslavia)

'is in grip of drink after upholding the very thing' is the wordplay.
'in grip of' means one lot of letters goes inside another.
'drink' becomes 'tot' (a small alcoholic drink).
'after' is a charade indicator (letters next to each other).
'upholding' says the letters should be written backwards (I've seen 'upheld' mean this).
'the very thing' becomes 'it' ('that's it!').
'it' reversed gives 'ti'.
'is' placed within 'tot' is 'toist'.
'toist' after 'ti' is 'TITOIST'.