If you want to keep your domain with your current registrar, and simply transfer the hosting to Mr.Host, then there is no extra charges, and no, you don’t have to pay for it again.
If you want to actually do a registrar transfer, and make Mr.Host your domain registrar, then there is a minimum of a one year renewal fee that goes towards the domain name. You don’t pay for it *again*, you just have to renew it for another year on top of what you already have- so you’re not losing anything.
Please see the Mr.Host Domain Pricing section for current domain pricing.