Now a complete answer, thanks to the clever idea of @Chrone in comments.
I start at one end of the table.
Carlsen (Magnus), current wold champion busy defending his title in a very tense match in London.
Replace my ending with a ton of ice, and I sip my beer.
The ton of ice must be an iceberg (although this is much heavier than a ton), and a Carlsberg is a Danish beer. (Karlsberg is also a german beer, but much less to my taste).
Then remove my ending, and I sit in a Scandinavian castle.
We remove 'sberg' and we get Carl, king of Sweden. Which one ? Pick your favorite.
Put a girl in between, and I walk around in my cassock.
Dina is a girl's firstname, and a Cardinal wears a cassock.
Round out D and make a large centralization, and I'm in America.
D rounded is an O, then the 'l' gets centralized and we get Carolina, the name of two US states.
An Odessa-hosted site replaces my middle.
The domain name for Ukrainian websites is .ua, which we put in the middle in place of 'oli' to get:
Now I'm at the other end of the table.
Caruana (Fabiano), Carlsen's challenger in the World Championship, conveniently sitting at the other end of the chess table.
What do you think is on the table?
A chessboard, a chess clock, some papers and pens, a lot of bottles of water, and 32-chess pieces - including bishops (wearing cassocks) and rooks (aka castles).