Born in Toronto, Ontario to Jamaican parents, Kaye first began playing soccer with Wexford SC in Scarborough.

[7] Kaye joined the Wilmington Hammerheads of the USL Pro on loan from TFC Academy in August 2014 as part of an affiliation between the two clubs.

[10] On March 12, 2015, Kaye and seven other players were signed by USL side Toronto FC II ahead of their inaugural season.

[13] On January 13, 2016, Kaye would sign with USL side Louisville City FC[13] and he would make his season debut in the opening match on March 26 against Charlotte.

[21] On July 26, 2018, Kaye suffered a fractured foot in the El Tráfico rivalry game against the LA Galaxy, with coach Bob Bradley saying he'd need surgery, with LAFC setting no timetable for his return;[22] NBC Sports reported that the injury would sideline the player for "4–6 months".

[23] On July 27, 2021, Kaye was traded, alongside a first-round pick in the 2022 MLS SuperDraft to the Colorado Rapids in exchange for $1 million in General Allocation Money and a 2022 international roster slot.

[25] On August 21 Kaye scored his first goal for the Rapids, netting the game-winner in a 2–1 comeback win over Rocky Mountain Cup rivals Real Salt Lake.

[28] In July 2022, Toronto FC announced they had traded Ralph Priso, General Allocation Money, a first round pick in the 2023 MLS SuperDraft and an international roster slot for Kaye.

[32] On July 13, 2023, Kaye was traded to the New England Revolution in return for Latif Blessing and a 2023 international roster slot.

[41] In July 2021 Kaye would join Canada for his third Gold Cup tournament, being named to the squad for the 2021 edition of the competition.