New Stampeder head coach Dave Dickenson announced his coaching staff Thursday.
Claybrooks was Calgary's defensive line coach for four seasons, so former Stampeder defensive tackle Corey Mace takes over at that position. Ryan Dinwiddie is the other newcomer as quarterbacks coach.
The returning coaches are Mark Kilam (special teams), Pete Costanza (receivers), Marc Mueller (running backs), Pat DelMonaco (offensive line), Brent Monson (linebackers) and Kahlil Carter (defensive backs).
John Hufnagel stepped aside as head coach after eight seasons, but will continue as general manager.
Dickenson has said Stubler's departure was unexpected.
"I wanted to keep as much continuity as I could as I feel our staff has done an excellent job under Huff,'' Dickenson said in a statement. "We have some young coaches who will be given more responsibility and I am confident that our coaches are ready and prepared.''
Claybrooks, 38, played two seasons for the Montreal Alouettes and three seasons for Calgary before stepping into the coaching ranks in 2012.
Under Claybrooks in 2015, Calgary's defensive line contributed to one of the league's top defences as the Stampeders ranked first in fewest points allowed per game (16.1), touchdowns (22), rushing touchdowns allowed (four) and average yards allowed per carry (4.6).
Mace will make his coaching debut with the Stampeders after six seasons as a player. The Vancouver native played 40 regular-season games and six playoff games, including the 2014 Grey Cup in which he recorded a sack.
Dinwiddie spent the last three years on Montreal's coaching staff. The Elk Grove, Calif., native was a co-offensive co-ordinator and running backs coach in 2015.
Dinwiddie played quarterback for the Winnipeg Blue Bombers for three seasons and Saskatchewan Roughriders for two.