Suggested a naughty child didn't tell the truth (7)
I believe the answer is:
implied
'suggested' is the definition.
(implying is a kind of suggesting)
'a naughty child didn't tell the truth' is the wordplay.
'a naughty child' becomes 'imp' (informal term for a misbehaving child).
'didn't tell the truth' becomes 'lied' (I've seen this in another clue).
'imp'+'lied'='IMPLIED'
(Other definitions for implied that I've seen before include "Suggested; not explicit" , "Unspoken" , "Stated indirectly" , "Insinuated, hinted" , "Understood" .)