Exclusion from old job (8)
I believe the answer is:
omission
'exclusion' is the definition.
(I've seen this before)
'old job' is the wordplay.
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'job' becomes 'mission' (a mission is a job or task).
'o'+'mission'='OMISSION'
'from' is the link.
(Other definitions for omission that I've seen before include "type of sin" , "Leaving-out, oversight" , "Something left out or forgotten" , "Something left out or neglected" , "Gap" .)