At home, deep in thought about former partner's budget (11)
I believe the answer is:
inexpensive
'budget' is the definition.
(I've seen this before)
'at home deep in thought about former partner's' is the wordplay.
'at home' becomes 'in' ('I'm in' can mean 'I'm at home').
'deep in thought' becomes 'pensive' (I've seen this in another clue).
'about' means one lot of letters go next to another.
'former partner' becomes 'ex' (an ex-partner).
'pensive' after 'ex' is 'expensive'.
'in'+'expensive'='INEXPENSIVE'
(Other definitions for inexpensive that I've seen before include "Cheap" , "budget" , "discounted" .)