move time machine to another hard drive

I recommend you not do that.

Time machine creates a complex database of saved files. Every time you do something to that database, you run the risk of introducing an error that causes the Time machine database to lose its intergity, and possibly lose your files.

I suggest a different approach.

Obtain a new drive, and ADD it as an Additional Time machine backup destination. Time machine will create a new stand-alone backup set on the new drive. Then while both are available, every-other backup goes to every-other drive.

After a week or so, you will have confidence that the new drive can carry you forward, and the old drive can be retired (set aside Or repurposed) at any time.

Barckus wrote:

move time machine to another hard drive

I want to copy or move the data from the current hard drive to a new hard drive. The old one is becoming less reliable, but I want to keep the backups

Start a new backup on your new drive.

<< I am trying to find a way to save the [old backups] and get rid of the old one >>

Add your new drive as a second drive, and keep using the old drive AND the new drive, together, for some period of time of your choosing.

If you copy the old backups to the new drive, you threaten to compromise the integrity of your surviving single backup going forward. that is not worth then minor possibility that you might need something older that is also NO LONGER on your current main drive or your new backup.