More subtle control upped following stir (7)
I believe the answer is:
cannier
'more subtle' is the definition.
(subtle can mean canny or shrewd)
'control upped following stir' is the wordplay.
'control' becomes 'rein' (reining is a kind of controlling).
'upped' says the letters should be written in reverse (in down clue, made to go up).
'following' is a charade indicator (letters next to each other).
'stir' becomes 'can' (I've seen this in other clues).
'rein' back-to-front is 'nier'.
'nier' after 'can' is 'CANNIER'.
(Another definition for cannier that I've seen is " more cute".)