A man to persistently annoy (5)
I believe the answer is:
harry
This clue could be a double definition.
'a man' is the first definition.
'persistently annoy' is the second definition.
'harry' can be an answer for 'annoy' (harrying is a kind of annoying). I am not sure about the 'persistently' bit.
'to' is the link.
Can you help me to learn more?
(Other definitions for harry that I've seen before include "Hassle" , "Persistently harass" , "Torment (a prince?)" , "English prince - trouble" , "Ravage - pester" .)