Reestablishing your WhatsApp account on a new device doesn't give access to your old chat messages, you need to restore a WhatsApp backup for that. The backup doesn't need to be stored in the cloud, you can choose to create a local file and manually transfer that to your new device.

In any case, as soon as you start using WhatsApp on a new device, users in the chats you participate in will receive a message informing them that your encryption keys have changed.