Proprietor in depression, heading off (5)
I believe the answer is:
owner
'proprietor' is the definition.
(I know that proprietor can be written as owner)
'depression heading off' is the wordplay.
'depression' becomes 'downer' (depression means feeling down).
'heading off' means to remove the first letter.
'downer' with its first letter taken off is 'OWNER'.
'in' is the link.
(Other definitions for owner that I've seen before include "possessive type" , "Holder, possessor" , "Person having property" , "One who has something" , "The person in legal possession" .)