Possessor of depressant losing head (5)
I believe the answer is:
owner
'possessor' is the definition.
(I know that possessor can be written as owner)
'depressant losing head' is the wordplay.
'depressant' becomes 'downer' (synonyms).
'losing head' means to remove the first letter.
'downer' with its first letter removed is 'OWNER'.
'of' is the link.
(Other definitions for owner that I've seen before include "The person in legal possession" , "One who has something" , "Holder, possessor" , "One that secured" , "Title holder?" .)