Northerner has zero hesitation getting a conveyance (7)
I believe the answer is:
scooter
'a conveyance' is the definition.
(scooter is a kind of conveyance)
'northerner has zero hesitation' is the wordplay.
'northerner' becomes 'scot' (someone from Scotland).
'has' means one lot of letters goes inside another.
'zero' becomes 'O' (O resembles 0).
'hesitation' becomes 'er' (sound made while hesitating - um, er).
'scot' enclosing 'o' is 'scoot'.
'scoot'+'er'='SCOOTER'
'getting' acts as a link.
(Other definitions for scooter that I've seen before include "motor transport" , "To score (anag)" , "Vehicle and child's toy" , "Moveable toy" , "it may need physical boost" .)