Many admit to being depressed (4)
I believe the answer is:
down
'being depressed' is the definition.
('down' can be a synonym of 'depressed')
'many admit' is the wordplay.
'many' becomes 'd' (Roman numeral for 500).
'admit' becomes 'own' (own can mean to admit or acknowledge).
'd'+'own'='DOWN'
'to' is the link.
(Other definitions for down that I've seen before include "Dispirited" , "In a low mood; hill" , "Depressed - Irish county" , "Out of sorts" , "drink at speed" .)