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Salisbury had been in charge of Sussex's Championship and 50-over team since November 2020, with Kirtley taking over the T20 set-up in the same timeframe following the departure of their predecessor Jason Gillespie.
However, with the club currently second-from-bottom in the County Championship and battling to avoid defeat in their final match of the season against Glamorgan, it is understood that Salisbury has been placed on gardening leave, due to his handling of the 21-year-old spinner, Jack Carson.
Carson, who debuted as a teenager in the Bob Willis Trophy in 2020, was Sussex's leading wicket-taker in both that competition and the 2021 County Championship. However, having missed the start of the 2022 season following knee surgery, all three of his appearances in the current campaign have come in the past fortnight, since Salisbury's departure.
That includes the ongoing contest against Glamorgan at Hove, but speaking to the BBC at the close of the second day's play, Kirtley was coy about the circumstances at the club.
"We can't make any further comment on that. There's a legal process that has to be followed," Kirtley said. "But it's an obvious distraction to the lads.
"We talk a lot about distractions," he added. "This is a time of year when contracts are negotiated, and for this young side, it's very important they understand that this is part of the game, and their ability to rise above those situations is a real skill."
The prospect of losing Carson - a highly-rated offspinner who was born in Northern Ireland but is England-qualified - comes in the wake of several high-profile departures from Hove in recent seasons, most recently the England duo of Chris Jordan and Phil Salt, but before them the likes of Reece Topley, Luke Wells, Danny Briggs, Laurie Evans, Michael Burgess and Harry Finch.
It is a talent drain that has come in for scathing criticism from the former Sussex and England wicketkeeper, Matt Prior, who renewed his attack on the club hierarchy - in particular the CEO Rob Andrew and director of cricket, Keith Greenfield - in a series of tweets on Tuesday evening.
"Another one the @SussexCCC Chairman, Board, Cricket committee, CEO and Performance Director will want to disappear very quickly," Prior wrote. "Not sure that's happening this time. The circle is closing around these people who have done so much to destroy our club."