Sarah's resolved to annoy (6)
I believe the answer is:
harass
'to annoy' is the definition.
(I know that harass is a more specific form of the action annoy)
'sarah's resolved' is the wordplay.
'resolved' is an anagram indicator.
'sarahs' is an anagram of 'HARASS'.
(Other definitions for harass that I've seen before include "hound" , "Annoy persistently, persecute" , "Molest, annoy" , "Bother and annoy continuously" , "Vex - pester" .)