You should try to perform the following tasks to add a new SIP domain
1) Add the new SIP domain in the existing Lync topology.
2) Publish the Topology and install the wizard on all the front end and edge servers.
3) Update your internal certificate with the new SIP domain entry through CA and then assign the new internal CA to the FE servers
4) Create the certificate for the new SIP domain and then install them on the edge servers and on the reverse proxy server .
For more details about each steps, you could refer to this article.
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