Delano Howell and Sergio Brown are expected to be among the competitors for Bethea's old job. An early round draft pick also could join the mix.
The Indianapolis defense also needs somebody to emerge as a pass-rushing threat opposite Mathis — who led the league with 19.5 sacks in 2013 and won the inaugural Deacon Jones award.
That man could be Adongo, a 24-year-old native of Kenya who was playing international rugby at this time last year.
"We know what he can do," Mathis said. "He has maximum work ethic. And he's going to be a big surprise in the league, I feel."
That's a pretty hefty prediction about a player who didn't make his NFL debut until last December. But Mathis sees a little of his younger self in Adongo. In fact, he has high hopes for both of the young pass rushers he's mentoring.
"They know the game," he said. "They can play a lot faster now. Last year was just trying to learn, find their way. They're here. They know what they're doing. So now it's just time to go get some quarterbacks."
Time weighs heavily on Mathis' mind these days. At 33, he's entering the final two years of his contract and perhaps his NFL career.
The Colts have improved from 2-14 in 2012 to 11-5 in each of the past two seasons. Indianapolis added a wild-card playoff victory in January, advancing one postseason step beyond the previous year.
It's slow and steady progress, but it might be time for a more rapid leap forward.
"We need to speed it up a little bit," Mathis said. "I'm kind of running out of time around here. I feel that we have the pieces in place. We just have to apply it."