Former partner is given short time to live (5)
I believe the answer is:
Here is my best explanation:
'live' is the definition.
('exist' can be a synonym of 'live')
'former partner is given short time' is the subsidiary indication.
'former partner' becomes 'ex'.
'given' is a charade indicator (letters next to each other).
'short' says to take the initial letters.
The first letter of 'time' is 't'.
'to' is the link.
(Other definitions for exist that I've seen before include "Have being or continue living", "Be alive", "Subsist", "Have life", "Have objective reality", "Be, live", "Are", "Having being", "Scrape by" and "Live".)