The Rangers midfielder has been called up for next month's Hampden double-header against Russia and Belgium.
Scotland boss Clarke announces his squad for the European Championship qualifiers at noon on Tuesday.
Jack will be back in after missing out for the squad for Clarke's first games in charge against Cyprus and Belgium in June.
The 27-year-old, who has two caps, has started nine of Rangers' 10 matches this season.
Speaking last week, Jack declared he would be excited about an international recall.
He told several newspapers: "First and foremost it is Rangers that I play for and that is where I need to be putting in good performances. If I get recognition off the back of that then I will be delighted."
Clarke picked a 27-man pool for his first two games but there are likely to be several changes.
Celtic goalkeeper Scott Bain will miss out with a dislocated thumb but team-mate Craig Gordon could return after recovering from a knee injury. David Marshall, who has conceded 12 goals in his first five games for Wigan, is likely to keep his place as number-one choice.
Clarke has some issues in central defence. Scott McKenna suffered a hamstring injury on Saturday which is likely to rule him out and his Aberdeen team-mate, Michael Devlin, is still to make his comeback after experiencing a similar injury six weeks ago. Hearts centre-back John Souttar has missed three games with an ankle injury but could be back this weekend.
In midfield, Graeme Shinnie has not featured in any of Derby's five Championship games since moving from Aberdeen. John Fleck, who missed the last squad because of his wedding, is on the sidelines with a hamstring complaint but could return for Sheffield United this weekend.
West Ham winger Robert Snodgrass declared himself open to a return to the set-up after drifting away from the international stage under Alex McLeish.
Up front, Steven Fletcher recently admitted he was contemplating international retirement after missing recent squads amid fitness issues, while Steven Naismith's comeback from a six-month lay-off was cut short by a hamstring problem. He too could return for Hearts this weekend.
Leigh Griffiths is keen to return after hitting three goals for Celtic following his return to football, while Cardiff's Callum Paterson is back in action following the ankle injury he suffered against San Marino in March.