Hi Dave,
Welcome.
Could you please list the brand and model number of your outboard? If you know the year model that might be helpful too.
If it is a Honda, and I'm assuming it is, they will have what is called a "frame number" that can be very useful for maintenance and identifying and ordering parts.
On older units (pre 2000) the frame number might be printed on a label located on the starboard or right side of the extension (leg) case. The post 2000 model frame numbers are typically found on the front portion of the part that clamps to the transom of the boat and can usually be easily read while sitting at the tiller.
An example frame number might look like:
BALJ-1000001
Always four letters followed by seven numbers.
Sadly, often those number labels have fallen off or have been intentionally removed. But if yours is there, you might want to write it down and keep a copy with the boat's papers for future reference.
As to your issue, the first thing I might have you check is the vent on your fuel tank. If it's an old style portable tank, it will have a small thumbscrew in the tank cap to vent the tank. If you forget to open it or, it has vibrated shut, it can cause the symptom you describe. Very common problem that's bitten all of us at one time or another.
If the vent is open then the next thing to consider would be the fuel hose and or bulb. If they are aged and possibly sun damaged from exposure, there could be crazing cracks in the hose and there could be air entering causing a loss of prime.
Inside the bulb is a check valve to prevent "backflow" of the fuel. On an old bulb it might be leaking. I have also found that laying the hose in such a way that the bulb lays horizontally and that you can see that the flow direction arrow is on top also helps to prevent loss of prime issues. Having the bulb hang vertically on the delivery hose will often cause loss of prime. The solution is to have enough hose on the outlet side of the bulb so that you can lay the bulb flat on the deck or the hull floor.
Check out those things and get back to us with what you find.
Hopefully others here will chime in with some good/better ideas.
Good luck.