Can I get my AirTag associated with my personal iPhone or Apple ID?

I have an AirTag that was associated with an AppleID for a work phone I no longer have (don’t work there anymore). I’ve reset the AirTag, but it’s still associated with that old AppleID. Can I get my AirTag associated with my personal phone/AppleID or do I just have to buy a new AirTag?

[Re-Titled by Moderator]