Fed up with primarily exorbitant lease, took a partner thoughtfully (13)
I believe the answer is:
deferentially
'thoughtfully' is the definition.
(both can mean respectfully)
'fed up with primarily exorbitant lease took a partner' is the wordplay.
'fed up' becomes 'def' ('fed' going up in a down clue).
'with' is a charade indicator (letters next to each other).
'primarily' suggests taking the first letters.
'lease' becomes 'rent' (synonyms).
'took a partner' becomes 'ially' (I can't explain this - if you can you should give a lot more credence to this answer).
The first letter of 'exorbitant' is 'e'.
'def'+'e'+'rent'+'ially'='DEFERENTIALLY'
(Another definition for deferentially that I've seen is " Respectfully".)