[5] Ahead of the 2018–19 season, Kaše was assigned to the Lehigh Valley Phantoms, the American Hockey League affiliate of the Flyers.

[6] In the 2019–20 season, Kaše scored his first NHL goal with the Flyers on 17 December 2019, in the second period of a game against the Anaheim Ducks.

On 12 August 2020, Kaše was loaned by the Flyers to return to the Czech Extraliga with HC Karlovy Vary until the commencement of the delayed 2020–21 North American season.

[7] He returned to North America for the remainder of the 2020–21 season, playing most of his games with the Lehigh Valley Phantoms and only one with the Flyers.

On 25 May 2021, Kaše returned to his native Czech Republic, after signing a two-year contract with ELH club, HC Sparta Praha.