Former nurse making offer (6)
I believe the answer is:
extend
'offer' is the definition.
('extend' can be a synonym of 'offer')
'former nurse' is the wordplay.
'former' becomes 'ex'.
'nurse' becomes 'tend' (I've seen this before).
'ex'+'tend'='EXTEND'
'making' is the link.
(Other definitions for extend that I've seen before include "Stretch out, say the hand of friendship" , "Make larger or longer" , "Provide challenge" , "Draw out" , "Carry on" .)