Break from driving with small puncture in Minehead (3,4)
I believe the answer is:
pit stop
'break from driving' is the definition.
I don't understand the rest of the clue.
(Other definitions for pit stop that I've seen before include "Break during motor race" , "period of service?" , "place where car can be serviced - with 31a" , "Break for fuel etc." , "for rest of travellers" .)