Do you let the turntable spin when putting down record and attach the clamp.

If your turntable is delt-drive you can damage it this way.

If it’s Direct Drive you can’t damage it, and you can change record and add/remove disc stabilizer on top of the record on the fly (with spinning platter if you like).

I press the stop button each time I change record. I put my disc stabilizer on the spinning platter (after I turn it on, not before). But I use ONLY direct drive turntables.

I don't think I want to attempt putting the periphery ring clamp on my VPI while it's spinning. With my direct drive turntables, I leave the power on but stop the platter from spinning when I change records.

Platter is always spinning for the session. No clamps or weights. 

Since for a DD turntable, there is no momentary sound quality degradation associated with operating the on/off switch, I do off my DD turntables between LPs. For any of the ones I own, they are back up to speed in seconds after re-start. I use a SOTA reflex clamp on 3 of the 4 DDs, so I feel the need to have the platter stationary for changing LPs, anyway. My Lenco is under control of a Phoenix Engineering Eagle power supply and Roadrunner tach. The motor is controlled at the Roadrunner, and it only takes a push-push of a tiny button to stop and start it. So there too I shut down the motor between LPs.  Thus ends yet another exciting topic for me.