However, for a safe migration I recommend to get the new hosting plan in time, at the latest one week before the present contract expires. Normally, the hosting details are sent immediately after acquiring the new plan enabling you to move your website to the new provider.

Sidestep: The domain name is not the same as the website domain
Some people think that migrating the domain name to a new registrar is the same as migrating the website itself. This is not so! The domain name is only a name that can be linked to a specific domain or web space at the hosting company. One could compare it to the fact that the address where you live does not comprise the home itself with all your stuff. At least part of it must available before you can give a house warming party at your new address. In the same way, your website needs web space (a domain) where all the files and probably a database can reside.