Debt rises after a recession, primarily (7)
I believe the answer is:
Here is my best explanation:
'debt' is the definition.
(I've seen this before)
'rises after a recession primarily' is the subsidiary indication.
'rises' becomes 'rears' (rearing is a kind of rising**).
'after' says to put letters next to each other.
'primarily' indicates taking the first letters.
The initial letter of 'recession' is 'r'.
'rears' put after 'ar' is 'arrears'.
(Other definitions for arrears that I've seen before include "In these, payment is overdue", "Amount unpaid", "If in these, the money is overdue", "Debt", "In these, one is behind with payments", "State of being behind with payments", "Total unpaid debt", "Overdue debt", "Back payments due on a debt" and "Outstanding payments".)