The Blues winger has been named in Gordon Strachan's inaugural squad for Scotland's friendly fixture against Estonia next week.
It is almost seven years since Burke last received international recognition from his country.
"It's brilliant and long overdue," said Clark when asked about the 29-year-old's call-up. ”I have got to say, in the last six, seven games, I think he has gone back to last season's form.
"The great thing for me with Chris is that his attitude and application, the smile on his face, doesn't change. From the first day I walked in the football club, he's just the same every single day.
"He knew deep down that the first half of the season hasn't been anywhere near it was last season. But he just kept working hard and pushing all the time. I am absolutely delighted he has got the call-up he deserves. Hopefully this is a new chapter in his life with a new international manager."
Clark admitted that he was surprised that last Burke wasn't selected for Scotland last season as he put in the performances that earned him Blues' Player of the Year.
"It was a surprise because I would have thought last season he should have been nailed on," he added.
"But that's not for me to say. It's other people's business who they pick and who they don't pick. But everyone at the football club is delighted."