Finished poking cheeky beggar (10)
I believe the answer is:
impoverish
'beggar' is the definition.
(I know that beggar is a more specific form of the action impoverish)
'finished poking cheeky' is the wordplay.
'finished' becomes 'over' (over can mean finished or ended).
'poking' is an insertion indicator (poke can mean to create a hole in).
'cheeky' becomes 'impish' (I can't explain this - if you can you should give a lot more credence to this answer).
'over' put into 'impish' is 'IMPOVERISH'.
Can you help me to learn more?
(Other definitions for impoverish that I've seen before include "beggar" , "Make poor" , "Spoil the quality of" .)