MANHATTAN, Kan.—After a restless retirement, coach Bill Snyder is ready to turn Kansas State into a winner again.

Three years after handing off a successful Wildcats program to Ron Prince, the 69-year-old and wispy-haired Snyder was hired to take charge of the school he transformed from college football’s biggest losers to national championship contenders. Prince was fired this month but is completing the season.

“The Kansas State family is in flux right now,” Snyder said at a news conference Monday. “I want to be able to help. I want to be able to soothe the waters. I’...

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