Gilmour completed a £9m summer deadline day switch to the Seagulls in a bid to kickstart his career after being frozen out of the first-team picture at Stamford Bridge following a less than successful loan spell at Norwich last season.
The 21-year-old made his first Brighton appearance as a late substitute in the 5-2 win over Leicester the weekend before last, but he now finds himself back in a position of uncertainty with the manager who signed him, ironically, having departed to take charge of his former club following the sacking of Thomas Tuchel.
“He’s a bit unlucky Billy, isn’t he?" said Clarke, who named the ex-Rangers youngster in his squad for the upcoming Nations League triple-header against Ukraine and Ireland.
"Obviously the manager has gone and Billy says he signed there to play for that manager, but he’s going to have to play for the next manager. That’s the business, that’s football.
"It’s down to Billy, how he trains and how he plays when he gets the opportunity to play for Brighton. That will determine how many minutes he gets in that team.
“It’s down to Billy and I have no doubts that he will do well, which is why he is in this squad.
“I haven’t spoken to him. I’ll wait until he comes up and have a wee chat with him, Saltcoats boy to an Ardrossan boy!”
Clarke dismissed suggestions that Gilmour may be regretting his move to Brighton, adding: “I think he was clear in his mind that he didn’t want to go out on loan again. He wanted more minutes because, going forward, he wants to be part of the Scotland squad and to do that you have to be getting minutes on the pitch and playing as much as possible. He wanted to make a permanent move.
"I think, first of all, he wanted to stay at Chelsea but he wasn’t given the guarantees that he’d get enough minutes, so he chose to move and then circumstances dictate that the manager he was going to play for has gone to Chelsea. Now he has to impress the next manager at Brighton.”