Customer parking right inside a lot (6)
I believe the answer is:
patron
'customer' is the definition.
(a customer of a business or service)
'parking right inside a lot' is the wordplay.
'parking' becomes 'p' (abbreviation on road signs).
'right' becomes 'r' (common abbreviation).
'inside' is an insertion indicator.
'lot' becomes 'ton' (I've seen this in another clue).
'a'+'ton'='aton'
'r' put inside 'aton' is 'atron'.
'p'+'atron'='PATRON'
(Other definitions for patron that I've seen before include "manager (13) [FRENCH]" , "Sponsor or benefactor" , "One gives financial or other support, to an artist say" , "one of the regular customers" , "Pot ran out for protector" .)