New TimeMachine backup on the same drive I have recently successfully cleaned my hard drive and restored data with the TimeMachine backup. Now I would like to prepare backup of "new" system. Do I have to clean the drive first?
If you're asking about multiple backup of the same Mac on another backup volume, then no, that's not possible as the Time Machine will backup the same Mac and effectively overwrite the most recent backup.

If on the other hand you're asking about backing up multiple (different) Macs on the same backup volume, that's possible. I back up 5 Macs onto my NAS regularly.