Driver of cart taking a road north — new girl going that way (7)
I believe the answer is:
drayman
'driver of cart taking a road north new girl going that way' is the definition.
'drayman' can be an answer for 'driver of cart'. I'm unsure of the rest of the definition.
'driver of cart taking a road north new' is the wordplay.
'driver of cart' becomes 'dray' (I can't justify this - if you can you should believe this answer much more).
'taking' says to put letters next to each other.
'road' becomes 'm'.
'north' says the letters should be written in reverse (in a down clue, letters go up or 'northward').
'new' becomes 'n'.
'a'+'m'='am'
'am' backwards is 'ma'.
'dray'+'ma'+'n'='DRAYMAN'
(Other definitions for drayman that I've seen before include "Horse-drawn cart driver" , "Carter" .)