Salisbury made his Davis Cup debut for Great Britain in 2021 and also competed at the 2020 Summer Olympics alongside Andy Murray.

As he had experienced injury problems during his junior career he was not heavily recruited by American colleges and the decision to offer him a spot at Memphis was a "gamble" on the part of head coach Paul Goebel.

[5] Salisbury made his ATP Tour main-draw debut at the U.S. National Indoor Championships partnering David O'Hare, losing to the Bryan brothers in the first round.

[10][11] He competed in the Australian Open with partner Rajeev Ram to defend their title, but they lost to Ivan Dodig and Filip Polášek in the final.

[19] Seeded second, he also won his second mixed-doubles Grand Slam title at the US Open, again with Krawczyk, defeating Marcelo Arévalo and Giuliana Olmos in straight sets.

[21] At the Miami Open, Salisbury and Ram reached the quarterfinals, losing to eventual champions Hubert Hurkacz and John Isner.

[22] He won the 2022 Monte-Carlo Masters with Ram defeating sixth seeded pair of Robert Farah and Juan Sebastian Cabal.

[26][27] They became just the second team to repeat as men's doubles champions at this Major in the Open Era other than Todd Woodbridge and Mark Woodforde who went also back-to-back in New York.

[34] Back alongside Ram, he reached the final of the Canadian Open in Montreal but lost to top seeds Marcel Granollers and Horacio Zeballos in straight sets.

[35] At the US Open, Salisbury and Ram went out in the third round to Nathaniel Lammons and Jackson Withrow, suffering their first loss at the tournament in four years after a run of 20 successive wins.