the starter engine is hooked

I have a seat leon tdi and I get hooked on the starter engine I wanted to know what checks I can do or what will it be

Hi nachoracing, if your starter is the same, try disconnecting the connector at the starter and applying direct current to the starter motor with the ignition switch on. If it doesn't stick, then the ignition switch needs to be repaired. If it sticks, then the starter solenoid winding needs replacing. There's another method to avoid replacing the solenoid, but it can damage other components. I'm an auto electrician

If by "engaged" you mean it stays engaged, it's either the ignition switch or the starter solenoid (or starter motor solenoid, I don't know what you call it), but it's easy to test. Make a wire with two ends, put one end on the nut coming from the battery and the other on the one coming from the ignition switch, and the other end on the battery. If it stays engaged, it's the solenoid.

I've had that problem with several vehicles, the starter motor would get stuck and wouldn't engage with the engine; you'd only hear a click. I disassembled them and cleaned them with gasoline because the carbon buildup was causing them to seize up. I reassembled them and they worked perfectly, but I don't know if that will be your case.

The problem isn't that it won't start, it's that when I do start it, I hear a noise like the pinion isn't shifting back