Even though you have permanent residency in the United Kingdom, to be able to use the ESTA visa, you need to be a British citizen and have a valid passport issued by the UK (or by any of the 38 countries in the VWP). As Pakistan is not part of the Visa Waiver Program, its citizens cannot therefore take advantage of the visa waiver program and will need to apply for a B-2 tourist visa with the US Embassy in Pakistan.
You could apply for an ESTA visa if you have dual British-Pakistani citizenship or if you have become a British citizen and have accessed the United States and applied for the ESTA with your UK passport.
