Married with ring that's outstanding (4)
I believe the answer is:
owed
'outstanding' is the definition.
('owed' can be a synonym of 'outstanding')
'married with ring' is the wordplay.
'married' becomes 'wed' ('wed' can be similar in meaning to 'married').
'with' says to put letters next to each other.
'ring' becomes 'o'.
'wed' put after 'o' is 'OWED'.
'that's' is the link.
(Other definitions for owed that I've seen before include "Had a duty to pay" , "Was due to pay" , "Outstanding" , "Was obliged to pay" , "Had an obligation to pay" .)