Our friends at the Red Team Journal posted a notional job descrition for a "Strategic Red Team Director". This provides a good list of what's needed on a Red Team, an what a Red Team should be on an organization. Yes, it's not pentesting.
Go read it.
This is an excellent opportunity for an experienced, forward-looking red teamer to build a world-class red teaming capability at a prominent global organization. The successful Strategic Red Team Director will lead the enterprise’s efforts in adopting and maintaining a system-wide view of threat-driven risks, with the goal of working with senior management to control these risks.