Turn on French writer’s son’s nanny (9)
I believe the answer is:
governess
'nanny' is the definition.
(I've seen this in another clue)
'turn on french writer's son's' is the wordplay.
'turn' becomes 'go' (a person's move in a board game).
'on' is a charade indicator (letters next to each other) (in a down clue, letters appear on others).
'french writer's' becomes 'verne's' (author Jules Verne).
'go'+'vernes'+'s'='GOVERNESS'
(Other definitions for governess that I've seen before include "Mary Poppins, perhaps" , "Supernanny?" , "Teacher" , "Becky Sharp, say" , "Duenna" .)