Essential to accept money, which is causing irritation (8)
I believe the answer is:
needling
'is causing irritation' is the definition.
'essential to accept money' is the wordplay.
'essential' becomes 'needing'.
'to accept' means one lot of letters goes inside another.
'money' becomes 'l' (L can mean 'pounds').
'needing' enclosing 'l' is 'NEEDLING'.
'which' is the link.
(Other definitions for needling that I've seen before include "Doing embroidery" , "Provoking or annoying by continual criticism" , "Goading or provoking" , "irksome" , "Aggravating" .)