A family of Microsoft word processing software products for creating web, email, and print documents.
Office must be installed on the new laptop. Licenses are actually tied to family members' accounts, not to specific devices.
The family member who is supposed to use the new PC should sign in to their account at https://account.microsoft.com/services and then install Office.
If you haven't already invited your family members to share the subscription, see https://support.microsoft.com/en-us/office/share-your-microsoft-365-family-or-premium-subscription-b389b9ce-3ae3-4a82-9017-39d79972fcba .