It's CLA-rence with a short 'a' at the beginning. And I think
Clarence comes from
Clare not the other way round.
Clara is CLAR-a in Britain (Clar rhymes with star). I only realised Americans said Claire-a when I noticed a lot of people on this board debating
Claire and
Clara as if they sounded the same with an 'a' on the end of
Clara.