Kingston could make his first appearance since mid-December against Hamilton this weekend after recovering from a hamstring injury.
The Ghana international is out of contract this summer and Jefferies is keen to see him return to the form he displayed upon his arrival at the Edinburgh club.
"He's like the rest of them who are out of contract," said the Jambos boss.
"They have this period to show me they want to play for the club and that they've got something to offer.
"They all have the opportunity to impress us, show they want to be there and work hard for the club.
"They will be rewarded if I think they've done so. That's their challenge between now and the end of the season."
Jefferies has warned Kingston he will know immediately if the playmaker is not fully committed to the cause.
He told the Edinburgh Evening News: "He's got to remember that I'm one of these managers who will soon know, with the experience I've got, if he's genuine. I'm sure he is.
"It will be good for everyone if he complies with the demands. It's about playing for the team and working hard.
"I've had a chat with Larry and we know the problems. I already said I'd like him back playing the way he was when he first came to the club."
Source: Team Talk