Shock permeates island — without cuts taxes shoot up (9)
I believe the answer is:
skyrocket
'shoot up' is the definition.
(thesaurus)
'shock permeates island without cuts' is the wordplay.
'shock' becomes 'rock' (rock can mean to shock or stun).
'permeates' means one lot of letters goes inside another (inserted letters permeate or go through others).
'island' becomes 'skye' (Scottish island).
'without cuts' becomes 't' (I can't explain this - if you can you should give a lot more credence to this answer).
'rock' going inside 'skye' is 'skyrocke'.
'skyrocke'+'t'='SKYROCKET'
'taxes' is the link.
I am not very happy about this link. It may belong to another bit of the clue.
(Other definitions for skyrocket that I've seen before include "Mushroom" , "Shoot up high" , "Increase very rapidly" , "seen to shoot up" , "Shoot up abruptly" .)