What couse the STARTER TO STAY ENGAGED

You don't say whether the starter is continuously cranking the engine or just spinning continuously or whether after starting the engine the starter switches off but remains engaged? Lack of detail makes it difficult to give anything but a general answer.

Certainly the starter should be removed and checked for damage and correct operation. The pinion might be tight on the helix, the solenoid could be tight, the return spring broken or the arm pivot seized. If the starter has been engaged while the engine has run at speed or for more than a few minutes the overrun clutch should be replaced.

In any case where the starter has remained engaged the ignition/starter switch and the drive mechanism in the steering column lock should be inspected for correct operation.