Private parking near New Orleans (8)
I believe the answer is:
personal
'private' is the definition.
('personal' is associated in meaning with 'private')
'parking near new orleans' is the wordplay.
'parking' becomes 'p' (**).
'near' means one lot of letters go next to another.
'new' indicates an anagram.
'orleans' is an anagram of 'ersonal'.
'p'+'ersonal'='PERSONAL'
(Other definitions for personal that I've seen before include "Of one's private life - nobody else's business" , "Wounding" , "Offensively intrusive" , "Belonging to an individual" , "Affecting an individual" .)