Press learning to support naughty child (7)
I believe the answer is:
implore
'press' is the definition.
(I've seen this before)
'learning to support naughty child' is the wordplay.
'learning' becomes 'lore' (both can mean tradition or knowledge).
'to support' is a charade indicator (letters next to each other) (in a down clue, some letters hold others up).
'naughty child' becomes 'imp' (informal term for a misbehaving child).
'lore' put after 'imp' is 'IMPLORE'.
(Other definitions for implore that I've seen before include "Beg earnestly, beseech" , "Beg earnestly, plead" , "Beg desperately" , "Ask earnestly" , "More lip (anag)" .)