Excuse offered by old lover meaningless almost (6)
I believe the answer is:
exempt
'excuse' is the definition.
('exempt' can be a synonym of 'excuse')
'old lover meaningless almost' is the wordplay.
'old lover' becomes 'ex' (I've seen this in other clues).
'meaningless' becomes 'empty' ('empty' can be similar in meaning to 'meaningless').
'almost' means to remove the last letter (most of the word but not all of it).
'empty' with its last letter removed is 'empt'.
'ex'+'empt'='EXEMPT'
'offered by' is the link.
(Other definitions for exempt that I've seen before include "Not subject to (eg taxation)" , "Freed from liability (to tax etc)" , "Not subject to, taxation say" , "Release" , "Immune - absolve" .)