Fellow left-back Tierney is also progressing at the Emirates, although Clarke is currently deploying the Gunners ace at centre-back in a back three.
The formation sees Tierney overlap wing-back Robertson, with Clarke championing the “overlapping centre-backs” philosophy developed by Chris Wilder at Sheffield United.
The Scotland manager’s formation also sees Manchester United midfielder Scott McTominay play at centre-back, a role he’s yet to fulfil in the first team at Old Trafford.
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“Between November and March I was thinking about what we were good at,” Clarke told the High Performance Podcast.
“Defensively we weren’t great and needed a change. I phoned my coaches and said, ‘We can’t go with a back four, I want to go with a back three.’
“I had never coached a back three in my life so it was a challenge for me and my coaches.
“The personnel we had – we had two of the best left-backs in world football, Tierney and Robertson, and had to figure out how to get them in the team.
“At that moment I didn’t think the centre-back options were great, so let’s pick three and see if that makes it better!
“My idea was that Tierney could play centre-back and I had this mad idea that Scott McTominay could play as one of the others.
“I had good midfield players and I wanted to get three or four into the team but had nothing great up front really.
“I had a really good conversation with Tierney to tell him he was going to be the best left-sided centre-back that Scotland had ever had.”
Scotland can still qualify for this year’s World Cup in Qatar – their first since 1998.
Clarke’s team need to beat Ukraine at Hamden Park on March 24 and then either Wales or Austria to book their place at the tournament.
On persuading Tierney to play at centre-back, Clarke said: “A myth had built up around Kieran that he didn’t want to come and play with the national team, which wasn’t correct.
“But I think he always felt that he was a better left-back than Andy Robertson.
“Every player thinks they’re better than the immediate competition and if you compare them, there isn’t a cigarette paper between them.
“I had to persuade Kieran that he was better than Andy and that’s why I trusted him to play left centre-back and not Andy.
“Now, that’s probably not strictly true but that’s how I had to sell it to Kieran. Now we’ve got the best overlapping centre-back in world football. It works.
“Selling that position to Kieran was important and it was a really good conversation, he asked a lot of really good questions.
“I told him I loved him and I wanted him to play there.”