We'd like to deprecate one of our service desk project so is it possible to disable new ticket creation through our service desk and add a message?
You can do this if you edit the permission scheme of that project in order to change the "Create Issue" permissions. You will probably want to remove at least the "Service Desk Customer - portal access" group from that permissions, and perhaps other users/groups/roles as well. That would prevent the creation of new issues in that project, but not restrict users from seeing their previous existing issues.
Then under the project administration page for that project, you can go to Portal Settings. There you can add an announcement when customers visit that portal to explain this is no longer active.
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