Part of the much-maligned transfer acquisition panel at the club, Pleat's role was reduced last year and he has now been offered the post of associate director.
Keith Burt becomes director of recruitment and scouting, stepping up from his role as chief scout.
Forest chief executive Mark Arthur told the club website: "We feel that the structure we have developed with Keith in his full-time role is well placed to take the club forward.
"I would like to thank David for the enormous contribution he has made.
"He remains a friend of Nottingham Forest and will always be welcome at the City Ground."