[7] On March 1, 2018, Cirelli was recalled by the Tampa Bay Lightning from the Syracuse Crunch of the American Hockey League.

[10] On April 12, 2018, Cirelli made his NHL Stanley Cup Playoff debut in a 5–2 Lightning victory over the visiting New Jersey Devils.

[11] On April 21, 2018, Cirelli recorded his first career playoff assist and point in a 3–1 Lightning series clinching win over the New Jersey Devils.

On April 29, 2019, Cirelli was selected to make his full international debut after he was named to the Team Canada roster for the 2019 IIHF World Championship, held in Slovakia.

[15] He helped Canada progress through to the playoff rounds before losing the final to Finland to finish with the Silver Medal on May 26, 2019.