Hayes, 28, spent last season in the New Jersey Devils organization, collecting three goals and six assists in 33 NHL games and two assists in three AHL contests with Binghamton.
A second-round draft pick by Toronto in 2008, Hayes has 54 goals and 55 assists for 109 points in 334 career NHL games with New Jersey, Boston, Florida and Chicago.
He has also played 123 games in the AHL with Binghamton and Rockford, totaling 36 goals and 42 assists for 78 points.
Trotman, 27, played 49 games for Wilkes-Barre/Scranton in the AHL last season, producing seven goals, 10 assists and a plus-24 rating. He also skated in three NHL games with Pittsburgh.
Entering his seventh pro season in 2018-19, Trotman has totaled 70 career NHL games with Pittsburgh and Boston, recording three goals and nine assists for 12 points. In 208 AHL contests with W-B/Scranton, Ontario and Providence, Trotman has 20 goals and 55 assists for 75 points.
Elliott, a 2015 AHL All-Star and a 2018 Olympic bronze medalist with Canada, returns to North America after two seasons in Europe.
The 27-year-old blueliner has skated in 234 career AHL games with Lake Erie and Milwaukee, notching 51 goals and 63 assists for 114 points. He has also appeared in 84 NHL games with Colorado, Arizona and Nashville, picking up eight goals and 16 assists.
Muse, 29, made 15 appearances with the AHL’s Lehigh Valley Phantoms last season, going 11-2-1 with a 2.46 goals-against average, a .919 save percentage and one shutout.
Muse has played 174 AHL games in his career, posting a record of 87-59-10 with a 2.64 GAA, a .915 save percentage and nine shutouts.