The reactor in question is the Pakistan Research Reactor-1 (PARR-1) at the Pakistan Institute of Science and Technology (PINSTECH) near Islamabad. It's a 10 MW pool-type reactor that has been in operation since 1965. HEU fuel for the reactor has been supplied by the United States. Normal core load contains about 6.5-7.5 kg of fuel.The exact amount of spent fuel that the United States would like to remove is unknown, but it appears that the reactor produced a few tens of kilograms of spent fuel.
U.S. attempts to remove spent research reactor fuel from Pakistan
A U.S. Embassy cable sent from Islamabad in May 2009, which was released by WikiLeaks, describes U.S. attempts to remove spent fuel of the Pakistan Research Reactor. According to the document, the government of Pakistan "agreed in principle to the fuel removal in 2007," but had made little progress since then. The New York Times reported that the fuel remains in Pakistan under IAEA safeguards.