When a person is registered for VAT the registration covers all of that person’s business activities and, in the case of a partnership, covers activities of other partnerships having the same partners. This is because it is the person who is registered, not the business activity.
A change in legal entity, e.g. from sole trader to company or from partnership to sole trader, would require a new VAT registration.
If there is a change in partners, e.g. a new partner joins or one leaves, a new registration is not required but HMRC must be notified of the change. All partners share joint and several liability for the VAT debts and obligations of the partners.