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On the left hand side, you will have a list of all the clients associated with that matter. On the right hand side, you have any other contacts related to the matter.
From the left hand side, choose the green 'Add Client' button to add a new line in to the client's side.
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IMPORTANT: Once you have created finance or trust transactions using this matter, you will no longer be able to update the primary client so it is recommended to set up at the start of a matter.
Once you have made those changes, save your matter details.
You can check the Primary Client after this by opening the Matter Details Gold tab and looking at the Primary Client listed at the top.