Kompany ended an 11-year association with Manchester City in May after captaining the club to an unprecedented domestic treble in English football.
The 33-year-old Belgium centre-back opted for a return to his boyhood club as player-manager but an anticipated fairy tale has not got off to the anticipated start, with Anderlecht fourth bottom of the Belgian First Division with two points from four matches.
Friday's trip to Genk is the start of a tough run of four matches that also includes fixtures with Standard Liege, Antwerp and Club Brugge.
First-team coach Simon Davies – formerly Manchester City's academy chief – will now lead Anderlecht from the sidelines, with Kompany functioning as captain.
"As players and staff we're trying to find which players suit the system better than some. There's always going to be change, especially at the start," Davies told a news conference.
"We're trying a new project here. It's not going to happen overnight. This is a playing style that's new to the football club.
"We need some stability and one of those things that's going to change straight away is Vinny is going to be captain from the next game. He's going to lead the team and really concentrate on being the player on matchday.
"This is one of the things that we're going to try. We work so well as a staff during the week. Vinny and the club have a vision and we all work to it as staff. But it's important he's a player on match day.
"If Vinny can be the best player in the league, which he is, and lead on the field and I can take the responsibility in terms of other things, how we play, if we need to change shape during the game – I will take that responsibility with the staff on the side.
"We're finding out about each other. This is a new and different situation. All we know is we're going to be successful. This is just another step and a little bit more learning about each other."
Kompany's commitment to a style of play akin to Guardiola's City template has come in for criticism but Davies insists Anderlecht will not divert from their chosen path because of poor results.
"He loves the club so much he wants to give everything he's got to the club. What's more important is he continues to be one of the players, be the leader and concentrate on matchday," Davies added.
"It's also important that I can help and assist with that so we have a leader on the pitch and a leader on the side. Vinny can concentrate on the grass and I can focus on the tactical decisions.
"What overrides this is we're so confident it's untrue. We want success and the fans deserve that."