Landscape painter's private room with PC (4,9)
I believe the answer is:
john constable
'landscape painter's' is the definition.
'private room with pc' is the wordplay.
'private room' becomes 'john' (slang term for toilet).
'with' is a charade indicator (letters next to each other).
'pc' becomes 'constable' (I've seen this before).
'john'+'constable'='JOHN CONSTABLE'
(Other definitions for john constable that I've seen before include "Haywain artist" , "English landscape painter, d. 1837" .)