Beg to go first after parking (5)
I believe the answer is:
plead
'beg' is the definition.
(thesaurus)
'go first after parking' is the wordplay.
'go first' becomes 'lead' (I've seen this before).
'after' is a charade indicator (letters next to each other).
'parking' becomes 'p'.
'lead' put after 'p' is 'PLEAD'.
'to' is the link.
(Other definitions for plead that I've seen before include "Appeal earnestly" , "Sue" , "Request" , "Beg or petition" , "advocate in court" .)