Drug addict finds employment beginning to rankle (4)
I believe the answer is:
user
'drug addict' is the definition.
(thesaurus)
'employment beginning to rankle' is the wordplay.
'employment' becomes 'use' ('use' can be a synonym of 'employment').
'beginning to' says to take the initial letters.
The first letter of 'rankle' is 'r'.
'use'+'r'='USER'
'finds' is the link.
(Other definitions for user that I've seen before include "One who works an appliance" , "One taking advantage" , "One who employs" , "Right long-established" , "Operator; exploiter" .)