Lass having left -- a source of irritation (4)
I believe the answer is:
gall
'irritation' is the definition.
(thesaurus)
'lass having left a source' is the wordplay.
'lass' becomes 'gal' (I've seen this before).
'having' is a charade indicator (letters next to each other).
'a source' indicates taking the first letters (source can mean a beginning or origin).
The first letter of 'left' is 'l'.
'gal'+'l'='GALL'
'of' acts as a link.
(Other definitions for gall that I've seen before include "Brass nedk or bile" , "Spleen or brass neck" , "This bladder is attached to the liver and stores bile" , "Irritate - presumption" , "Bold impudent behaviour; abnormal growth on tree" .)