When a new president assumes office the matter of protocol arises for senators appointed by the previous president. For what it's worth, I offer the following comments.
The situation occurred when President Noor Hassanali assumed office in March 1987 in succession to President Ellis Clarke. Sir Ellis had appointed the senators barely two months before and they pondered whether they should resign, or at least offer their resignations to President Hassanali. I was requested to get President Hassanali's thoughts. President Hassanali saw no reason that senators appointed by President Clarke should resign.