Stress coming after former partner gets part of the house (9)
I believe the answer is:
extension
'part of the house' is the definition.
'stress coming after former partner' is the wordplay.
'stress' becomes 'tension' (synonyms).
'coming after' is a charade indicator (letters next to each other).
'former partner' becomes 'ex'.
'tension' put after 'ex' is 'EXTENSION'.
'gets' acts as a link.
(Other definitions for extension that I've seen before include "Added part" , "telephone number" , "more rooms in house maybe" , "Another phone" , "Additional time for repayment" .)