There is a filter inside the carb itself that can get clogged.
The primer does not pump fuel into the carb, it draws AIR out and pumps that expelled air back into the fuel tank.
When all of the air is gone the primer starts to pump fuel.
Unlile on a mower where the primer floods the carb on a hand held it PURGES air out of the system so the carb's inbuilt fuel pump can work.
The fuel pumps can not pump air.
After a couple of pulls the fuel tank pressurises and normal fuel pumping can occur.
Some carbs have a check valve in the carb, some have a few while others rely upon the duck bill valve in the primer.
When not used for a long time the check valves can get gummed up and the filter in the tank can break down allowing fibres into the carb which blocks the internal filter.
The float valve ( called a metering chamber valve ) is vitton tipped thus very prone to sticking in the closed position .
When you have finished with the equipment it is always a good idea to tip the fuel out and then run the carb dry.