I have changed from a MacBook Air to a new Macbook Air and want to use my existing external hard drive to continue backing up my new computer from where the old one left off. Will the back up continue or will it wipe the existing data?

Will the back up continue

It can, yes. Apple describes this in If your new Mac inherits your backup history

You can select this option after your new Mac has finished being set up, or (from memory) the next time your insert your Time Machine external disc for a backup. Note though that if you do this the backups cannot be used again for the old Mac.

In practice though I've found that the continuity of backups sometimes fails. My policy is to buy a new external drive and start again in my new system, retaining the old disc for a short time. This also gives the new disc a longer life, compared with the old one which no doubt has seen some heavy-duty use over the previous few years.

Your new Mac will have a USB-C port and your old USB cable might not be USB-C, so this would be a good time to switch to a new drive with a USB-C cable, rather than invest a fair whack of money for a connector which might be put to better use in funding a new drive with a USB-C cable

Personally, I would just use Migration Assistant to restore data from your Time Machine backup and then wipe the Time Machine drive and start over, unless there is some reason you may want to recover a file you may have deleted two or three years ago.

As others have stated keep you old drive just in case and get a new drive for the new backup. If you use the old drive and want to access the old Mac files you will see that it will not go back in time by just scrolling but you can access them by using shift-command-c

Hi,

If your new MacBook Air is Apple Silicon base, you'd better wipe the existing data from external drive to be avoidance the trouble.