The match was due to take place on March 24 but was postponed following Russia’s invasion of Ukraine.
Should Scotland beat Ukraine, they will face Wales at the Cardiff City Stadium on Sunday, June 5 for a place at this year’s World Cup in Qatar.
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Clarke’s side will also play three Nations League matches in June, with two scheduled games against Armenia, either side of a match against Republic of Ireland in Dublin.
Despite being called up to the Scotland squad for the first time in March, Stewart, 25, didn’t make his debut for the national side.
When asked about his international experience last month, Stewart told the Echo: “I loved it.
“Going away and representing your country and even just the training side and playing with players of that quality who were at the camp, it’s what you want to do as a player. It’s what I’ve wanted to do since I was a kid.
“Hopefully it happens again in the future but I know for that to happen I have to do well for my club, so I’ll just keep trying to do that and hopefully that will happen.”
Stewart scored his 26th goal of the season for Sunderland as the Black Cats beat Wycombe 2-0 in the League One play-off final at Wembley.