A lot of cheeky hacking going on (11)
I believe the answer is:
persevering
'going on' is the definition.
(persevering is a kind of going on)
'a lot of cheeky hacking' is the wordplay.
'a lot of' means to remove the last letter (a lot of the word but not all of it).
'cheeky' becomes 'pert' (pert can mean cheeky or insolent).
'hacking' becomes 'severing' (I am not sure about this - if you are sure you should believe this answer much more).
'pert' with its final letter taken off is 'per'.
'per'+'severing'='PERSEVERING'
Can you help me to learn more?
(Other definitions for persevering that I've seen before include "Soldiering on" , "Steadily continuing a task despite difficulties" , "Continuing in spite of difficulty" .)