Clingan has signed an 18-month deal after the 29-year-old was released by Doncaster last month.
Clingan, who has 33 international caps, started his career with Wolves before playing for Chesterfield, Notts Forest, Norwich and Coventry.
He is eligible for tonight's SPL clash at Parkhead but is not expected to feature.
Shiels said: "Sammy is a good player. He passes the ball well, gets into good positions and knows the game.
"He hasn't really played this season and needs to get some fitness and game time.
"There have been circumstances why he hasn't played but we will get him back in training."
Shiels promised to go with youth at Celtic Park, where Killie won for the first time in 57 years earlier this season, as the Ayrshire side negotiate three games in seven days.
The heavy schedule began with a goalless draw at Dundee on Sunday and ends with the William Hill Scottish Cup fifth-round visit of Inverness on Sunday.
Shiels said: "We will give the kids a go, it's a development game for us.
"We will throw in five teenagers. We have got it planned out what we are going to do.
"It's a long-term plan that I have.
"Hopefully they give a good performance and learn from mistakes and the experience.
"We are resting quite a few of the senior players.
"We had a hard game on Sunday on a heavy surface."