Should I remove the original sticky tape before applying new tape to sensors?

I removed my ring sensors and need to re-apply them in my new apartment. I got 3M double-sided tape to do so. But I'm wondering, should I remove the old adhesive, that originally came on the sensors, before applying the new double-sided tape? Or should I just put the tape on top of the old adhesive? Also, any tips on making sure these stay up good enough? I'm so afraid of them falling down and setting off the alarm!