How do you turn on encryption on a Time Machine drive?

System Preferences>Time Machine>Select Disk and tick the bottom left hand corner box.

NOTE: that you may have to unselect the disk and then reselect it.

I must do that myself at some point. Never bothered, and no idea why

I recently did it on a new SSD external but according to the following you can also do it later without losing data as long as it is locally connected: https://support.apple.com/guide/mac-help/keep-your-time-machine-backup-disk-secure-mh21241/mac

See the following from the previous link:

When you switch locally connected disks (such as an external disk) to encrypted backups, your data is preserved and encrypted.

If you want to change from unencrypted to encrypted backups, you must remove your backup disk and then set it up again. Follow these steps:

1. On your Mac, choose Apple menu  > System Preferences, then click Time Machine.
2. Click Select Disk or Add or Remove Backup Disk (if you have multiple backup disks).
3. Select your backup disk, then click Remove Disk.
4. Set up the disk again as an encrypted backup disk.

Certainly let the current backup end. Mine is greyed out too, and I think it is because encryption can only be selected at the time of selecting the disk (0.9 probability). I do know it can be applied retrospectively. I'm not sure what then time overhead is of switching it on. I think there is no real overhead once it is deployed

I've struggled to understand why I need to do it. I backup to a NAS and I have no problem in smashing faulty NAS drive. My MBP has encrypted SSD

[edit] No, I will not. See italics. "The best way to keep your backups secure is to encrypt your backup disk. When you switch a Time Capsule or network backup disk from unencrypted to encrypted, your existing backups are erased and new encrypted backup sets are created. When you switch locally connected disks (such as an external disk) to encrypted backups, your data is preserved and encrypted."

Re: I've struggled to understand why I need to do it. I backup to a NAS

Not sure if this is what you meant, but I backup to a USB connected SSD and I use FileVault on it only to protect the data in the event of a theft of the SSD.

I suppose it depends on whether the backup drive ever leaves one's direct control, or whether there is a risk of that.

With FileVault switched on and adding encrypted TM backup as to it as well one might say it was belt and braces, though👀

If you mean FileVault turned on in your internal main drive, note that when that is backed up (whether via Time Machine, 3rd party apps such as Carbon Copy Cloner, or online backup services), the backup is not protected.

Because TM has always been peculiar in that regard. I'm sorry, there is no better answer that I know of.

Do note the caveat if your TM drive is a NAS or a Time Capsule that your backup will be erased and will start all over again

It encrypts the entire drive (present and future contents) without erasing your data.