Transferring use of My Passport for Mac from one Mac Device to Another

Hello. I have recently purchased a 2T My Passport Ultra for Mac (WDBKY) and have used it to back up via Time Machine my IMac. I have now purchased a new MacBook Pro and have set this up using the Migration Assistant tool. I now want to transfer the use of my portable My Passport Ultra for Mac to my new MacBook Pro and use with Time Machine. I don’t want to use a restore as the two systems are now different.
Do I just plug in to Macbook or do I need to do anything to it to remove old backups?
Thanks for any advice and apologies if this is a stupid question.

Hi Rowens,

You can setup the Time Machine Backup on your WD My Passport for Mac using your MacBook Pro from the link given below.

You can either delete the old Time Machine backup from the drive manually by accessing the drive or keep it in the drive and setup the Time Machine of your New MacBook Pro as well. Configuring the Time Machine Backup of two different Mac will create the different folders in the drive.