Something left out from old assignment (8)
I believe the answer is:
omission
'something left out' is the definition.
(I've seen this before)
'old assignment' is the wordplay.
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'assignment' becomes 'mission' (mission is a kind of assignment).
'o'+'mission'='OMISSION'
'from' is the link.
(Other definitions for omission that I've seen before include "Something left out or not done" , "type of sin" , "Act of leaving out" , "Leaving-out, oversight" , "cut?" .)