You just need to point the name servers of the new hosting to the domain to get the domain showing data from the new hosting but if you are using Emails and other DNS services, you will need to point and set up all of these as well.
If you have a lot of traffic and don’t want your website to get down if you make any mistake, I suggest contacting the new hosting provider for help and they will help you out setting up everything. This is a delicate process else your website will be down for hours.
Let me know if you have any other question.
Hope it helps.
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