my guess is the needle and seat in the carb.
Has happened to me many many times before. Will be sticking etc. Best bet is to take the top of the carb off SLOWLY and remembering where everything goes, because there are a lot of things, linkages etc etc then checking the needle and seat.
Some have a mesh type filter just before it and can get clogged if crap gets through the fuel filter. Or the needle and seat might just be worn or old and doesnt want to work.

Other than that, if the pump is still pumping fine and the filter isnt clogged, then its either a block in the fuel tank breather creating a low pressure in there or a block in the fuel tank pickup. Possibly even a perished fuel line...

Id be checking the needle and seat first, for sure