Hotspot isn’t working

The first thing to do is to check Settings > General to see if either an iOS update or a Carrier update is available.

The next thing is to go to Settings > General > Reset > Reset Network Settings (all the way at the bottom of the General options) and do that reset. This will clear out your old network carrier's cellular settings that may be preventing this from working.

If that doesn't work the next likely issue is that your new carrier may not support Personal Hotspot. This is a carrier-dependent feature, and if the previous two suggestions don't work, it is likely the carrier. To confirm whether your carrier officially supports this you can refer to this comprehensive list of carriers and features that Apple provides:

Wireless carrier support and features for iPhone in the United States and Canada - Apple Support

(you can select another country on that page if you aren't in the US/Canada).

If it looks like your new carrier does support Personal Hotspot you will need to go to your carrier's support page to see what cellular settings you may need to manually set on your iPhone. Usually this is listed under BYOD (bring your own device) or "APN Settings" for iPhone in their support page. If you can't find that you'll need to contact them on the phones directly to find out what APN settings you should be using.

I am having the same issue and your solution fix it.

Thanks

Awesome! (hopefully it will work for the original poster too!)