I have a shallow well pump there is no check valve my pump is starting every 7 to 12 seconds water keeps droping if I install a check valve do I have to replace the foot valve

The foot valve acts as a check valve so it may have dirt in it or be bad. You can install a check valve but if the foot valve is open, it will still drain out the down pipe. I assume you only have 1 pipe..

Could be a really large leak in the wellpipe, but probably the footvalve is bad. If it is truly a shallow well system, then you don't have much more than 20 feet of well pipe. Should be able to pull it without too much trouble, especially if it is PVC.