Turned down rubbish date (7)
I believe the answer is:
refused
'turned down' is the definition.
('refuse' can be a synonym of 'turn down')
'rubbish date' is the wordplay.
'rubbish' becomes 'refuse' (both can mean waste material).
'date' becomes 'd' (common abbreviation eg in DOB, date of birth).
'refuse'+'d'='REFUSED'
(Other definitions for refused that I've seen before include "Was unwilling to accept" , "turned down appeal" , "Not accepted" , "Said no (7)" , "Declined, rejected" .)