Do i need a tank?

I Am installing a new well and cant get pump to stay primed. I do not have a tank is this my problem. Pump cavatates when first turned on. when i open discharge pump runs but minimal pressure. i have a 1/2 horse red lion pump. from pump to tip of point it is 24 feet. from pump to water it is 20 feet. This well is for a sprinkler system only.

Any help would be great.

OK...is it a new well or a new well pump or both?

I think you will find that 20' of suction lift is more than that pump can handle.