Private left yard on the sly (8)
I believe the answer is:
secretly
'on the sly' is the definition.
('secretly' can be a synonym of 'on the sly')
'private left yard' is the wordplay.
'private' becomes 'secret' ('secret' can be similar in meaning to 'private'**).
'left' becomes 'l' (common abbreviation).
'yard' becomes 'y'.
'secret'+'l'+'y'='SECRETLY'
(Other definitions for secretly that I've seen before include "On the q.t" , "in camera" , "Undercover" , "On the quiet" , "Clandestinely" .)