To add clients or related Contacts to Matters, when on the Matter’s Dashboard, click on Settings -> Edit 

Once you are on the Settings page click “Edit” in the Contacts section. 

Edit Matter Contacts window will pop up. Click on the “Add Contacts”.  

Populate both the Contacts and the Contact Type fields (You can customize the list of Contact Types, see more here: Contact Types).

Note that you must choose an existing Contact from the drop-down menu, you cannot add a new Contact from this screen ( see how to add a new Contact here: Contacts ).

When you populated the Contact and Contact type field click “Save”.