Harass or strain in pursuit of naughty child (9)
I believe the answer is:
importune
'harass' is the definition.
(I've seen this before)
'or strain in pursuit of naughty child' is the wordplay.
'strain' becomes 'tune' (synonyms).
'in pursuit of' means one lot of letters go next to another (some letters chase after others).
'naughty child' becomes 'imp' (informal term for a misbehaving child).
'or'+'tune'='ortune'
'ortune' put after 'imp' is 'IMPORTUNE'.
(Other definitions for importune that I've seen before include "Make insistent requests for entropium" , "Harry" , "plague" , "Persistently request" , "press to give answers" .)