Persistently annoy prince (5)
I believe the answer is:
harry
'persistently annoy' is the definition.
'harry' can be an answer for 'annoy' (harrying is a kind of annoying). I am unsure of the 'persistently' bit.
I can't explain the rest of the clue.
Can you help me to learn more?
(Other definitions for harry that I've seen before include "Ravage - pester" , "Make repeated attacks on, badger" , "Ravage - prince" , "Wizard Potter" , "Persistently harass" .)