Irritating demand by Heather (8)
I believe the answer is:
needling
'irritating' is the definition.
'demand by heather' is the wordplay.
'demand' becomes 'need' ('need' can be a synonym of 'demand').
'by' says to put letters next to each other.
'heather' becomes 'ling' ('ling' can be a synonym of 'heather').
'need'+'ling'='NEEDLING'
(Other definitions for needling that I've seen before include "Aggravating" , "irksome" , "Provoking or annoying by continual criticism" , "Doing embroidery" , "Goading or provoking" .)