Increase waste when former partner is home (9)
I believe the answer is:
Here is my best explanation:
'increase' is the definition.
('increment' can be a synonym of 'increase')
I don't understand the rest of the clue.
(Other definitions for increment that I've seen before include "Increase (one of a series)", "additional pay", "Addition to wages etc", "Step", "Small addition to salary etc", "growth", "Amount by which something increases" and "Rise".)