The only real need on the logistics front is for a boom-capable tanker to operate with the F-16s. Seeing the limited use of boom-type refueling, it is not surprising that options on this front are severely limited.
The only ones making boom probes are Boeing, Airbus DS and IAI. Unfortunately, Boeing and Airbus DS are focused on securing sales for their flagship platforms - i.e. KC-46 and A330 MRTT - and probably won't sell the boom-probe as a stand-alone product for a bespoke solution. IAI would do it, but Pakistan can't be a direct customer.
On the other hand, there is the option of making a bespoke/custom hose-and-drogue refueling aircraft.
I know the PAF has the IL-78, but I doubt the IL-78 can best a commercial airliner in fuel efficiency. For the task of air-to-air refueling, you want the tanker to preserve as much fuel as possible. The PAF has the theoretical option of looking at mothballed or used airliners and configuring them with Cobham Wing Air Refueling Pods (WARP).