Striker Cumbers and defender Wynter both had options on their initial one-year deals taken up by the Gills, while striker Pugh has agreed a new one-year deal but is yet to officially sign it.
Both Cumbers and Pugh have featured for the first team before, while Wynter has been named on the bench once and has travelled with the squad for away games on numerous occasions last season.
Stimson told KentOnline: "Luis Cumbers and Andy Pugh are two young players who unfortunately since I've been at the club have had a nightmare with injuries on and off.
"But I've certainly seen something in them to offer them another year and hopefully they can stay injury free throughout pre-season and they can push the senior players. They've both shown for the reserves that they have an eye for the goal.
"Tom Wynter is an honest defender and he went out on loan a few times last season. Sometimes you can make a decision too early with young players and he's now got a bit longer to show me what he's got. He's a strong defender and a good character."