Having played for Bermuda at various age levels,[3] Leverock made his debut against Argentina in the 2011 ICC World Cricket League Americas Region Twenty20 Division One.

[12] On 3 June 2018, he was selected to play for the Vancouver Knights in the players' draft for the inaugural edition of the Global T20 Canada tournament.

[13][14] In August 2019, he was named in Bermuda's squad for the Regional Finals of the 2018–19 ICC T20 World Cup Americas Qualifier tournament.

[16] In September 2019, he was named in Bermuda's squad for the 2019 ICC T20 World Cup Qualifier tournament in the United Arab Emirates.

[19] In October 2021, he was named as the captain of Bermuda's squad for the 2021 ICC Men's T20 World Cup Americas Qualifier tournament in Antigua.