Faced with demand, was first to be irritated (7)
I believe the answer is:
needled
'be irritated' is the definition.
(I've seen this before)
'faced with demand was first' is the wordplay.
'faced with' is a charade indicator (letters next to each other).
'demand' becomes 'need' ('need' can be a synonym of 'demand').
'was first' becomes 'led'.
'need' put next to 'led' is 'NEEDLED'.
'to' is the link.
(Other definitions for needled that I've seen before include "Irked" , "Goaded or provoked" , "Provoked with sewing implement" , "Annoyed - provoked" , "Irritated (sl.)" .)