Young hooligan goes round a horse, childishly worried (6)
I believe the answer is:
nagged
'worried' is the definition.
(nagging is a kind of worrying)
'young hooligan goes round a horse childishly' is the wordplay.
'young hooligan' becomes 'ned' (informal term for a troublemaker).
'goes round' means one lot of letters goes inside another.
'horse childishly' becomes 'gg' (gee-gee is a childish word for horse).
'a'+'gg'='agg'
'ned' placed around 'agg' is 'NAGGED'.
(Other definitions for nagged that I've seen before include "Persistently harassed" , "Scolded continuously" , "Constantly scolded or found fault with" , "Constantly pestered" , "Found fault or scolded continually" .)