A tourist with a foreign passport can not buy a vehicle. Con Artists / Scammer may guide you otherwise.
There exist no licensed registered vehicle rental services. On top of that the private rentals for Self-Driven vehicles does not offer any insurance (though insured) so they can juice out more incase of any breakdown. Pakistan is a nightmare in terms of car rentals. Law does not provide any cover for Self-Driven Rentals. a nightmare you can read here
We strongly discourage self-driven rental instead recommend strongly to rent a vehicle with driver. That way you get 2 strong advantages when you hire a vehicle with a driver.
a). Long Term & Short Term charges can be negotiated, fueling is as per usage. there is no advance down payment required. (as human you can treat the driver for food otherwise not obligatory)
b). Incase of breakdown the alternative vehicle is provided at no extra charge.
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Arrive Karachi, contact Mandviwalla Car rental Mr. Adnan. He can provide you rental vehicles with driver in almost every major city of Pakistan. go around in rental vehicles. @KamranAslam may also be able to help.
for Northern areas & Kashmir you can hire a SUV from RWP/ISB. go around complete the tour and return vehicle in RWP Airport drop they will do complimentary . Take flight back home from there.
@asifcae & @HanifBhatti @tourist are columbus of Pakistan touring scene. They can tell you in their sleep for areas & best time of year to go around.