There are 3 options to update a stakeholder with a new Contact Group:
Use Stakeholder Search to find the relevant stakeholder records and manually update each stakeholder's Contact Group details (remember you can have several stakeholder records open at the same time in multiple tabs).
Within Admin / Contact Groups: Highlight the new Contact Group and select Link Stakeholder to link required stakeholder.
3. If there are a large number of stakeholders to be updated, use Stakeholder Search to find the relevant stakeholders and then use the export to transfer them into Excel. Within Admin / Import: Stakeholders: download the import template and then cut and past First Name / Last Name of the required stakeholders from the Stakeholder Excel export spreadsheet and paste them into the Import template and add the new contact group detail. Then complete the import and the records will be updated with the new contact group.