Kostka was signed as a free agent by the Senators this past July but has yet to play a game with the club. The 30-year-old has played in 70 NHL games in the past three seasons with the Toronto Maple Leafs, Chicago Blackhawks, Tampa Bay Lightning and New York Rangers.
He's scored 20 points in that time and is a career plus-4.
This year, he leads Binghamton in plus-minus (10), and is the second highest scoring defenceman on the team with 12 points (1G, 11A) despite playing in only 23 games.
Claesson was drafted 126th overall in 2011. In 29 games with the B-Sens, the 23-year-old has eight points (2G, 6A) and 38 penalty minutes.
The 6-foot-1 native of Stockholm has never played in an NHL game, and could become the eighth player from Ottawa's 2011 draft class to do so should he get to dress during this call-up.
The Senators host the New Jersey Devils Wednesday night.