Discharge former partner on Greek island (7)
I believe the answer is:
Here is my best explanation:
'discharge' is the definition.
(excreting is a kind of discharging)
'former partner on greek island' is the wordplay.
'former partner' becomes 'ex'.
'on' means one lot of letters go next to another.
'greek island' becomes 'crete' (I've seen this before).
(Other definitions for excrete that I've seen before include "Eliminate (from the body)", "Defecate" and "Expel (waste) from the body".)