Sign on new private door (7)
I believe the answer is:
postern
'private door' is the definition.
'postern' can be an answer for 'door' (I've seen this before). I'm not certain of the 'private' bit.
'sign on new' is the wordplay.
'sign' becomes 'poster' (poster is a kind of sign).
'on new' becomes 'n' (common abbreviation eg NT for New Testament. I am not sure about the 'on' bit.).
'poster'+'n'='POSTERN'
Can you help me to learn more?
(Other definitions for postern that I've seen before include "Rear entrance" , "Small gate in the rear of a fort or castle" , "Back or side entrance" , "a way in the back" , "Back door eg of castle" .)