Unable to update TikTok because it is connected to my old iCloud account

You have not described any issue that needs fixing. If you download TikTok with a previous Apple ID, you can only update that app with that Apple ID. Of course you can delete the TikTok app downloaded from a previous Apple ID and download TikTok again with the current Apple ID if that is what you want to do.

There are many reasons that you may not be able to update an app with your Apple ID, and that does not mean that anything needs fixing. It may be working exactly as Apple has designed it to work.

If you can’t download or update apps on your iPhone or iPad - Apple Support

DaniiJP wrote:

it is connected to my old iCloud

Each person requires her/his own, unique Apple ID (which is what “connected to my old iCloud” means).

A different Apple ID (connection to iCloud) looks like a different person.