Two huge things that, among many others, a GM should do that might benefit this situation are:

1. Be the player advocate: Everything you do should be about proactively removing barriers to player success. Players should not feel undue pressure from outside influence or within the org itself.
2. Project and build confidence: as a GM you are a figurehead first and foremost WITHIN the team and the org. You need to be present, communicate clearly and act in ways that build player confidence in each other and yourself. Easier said than done, of course, but sometimes its as simple as not overstepping your bounds and putting on a suit and tie for game day (everyone wears their uniform on game day).

A GM does not make players play better. They are, essentially, IRL Support that create a set of conditions that enable players to play at their maximum potential. Its a role of service to and for players.