Naughty child didn't tell the truth, it's suggested (7)
I believe the answer is:
implied
'suggested' is the definition.
(implying is a kind of suggesting)
'naughty child didn't tell the truth' is the wordplay.
'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'
'it's' is the link.
(Other definitions for implied that I've seen before include "Suggested; not explicit" , "Insinuated, hinted" , "I limped in hinted or suggested way" , "Understood" , "Indicated by suggestion" .)