Clarke led the Baggies to eighth place last season, which is the club's highest finish in the Premier League.
However, West Brom won just once in their final nine games of the campaign.
While Peace admits that the team's end-of-season form was a slight disappointment, he has declared himself pleased with the club's overall progression under Clarke.
Peace told the Express & Star: "He has done well. We had a great start and a very indifferent finish – apart from the last game which was something to behold.
"Everyone's pleased with how it's turned out and we have progressed on and finished eighth. Steve has another year left on his existing deal.
"We will sit down over the next few months and discuss where we go with that. His contract is well structured, he gets rewarded for improvement and where we finish in the league. He's been very good. You cannot knock what he did."
Clarke began his coaching career in 1998 as Ruud Gullit's assistant at Newcastle United, where he spent a brief spell as caretaker manager in 1999.
He occupied coaching roles at Chelsea, West Ham United and Liverpool, before being named as West Brom boss in June 2012.