When starting a newly-established C-suite position, what are the critical factors executives should consider to establish themselves and drive results?

Listen.  The single most critical thing you can do the first few weeks is to listen - to everyone.  You are entering the position with a clear (or murky) preconceived notion of how things are - but that has been painted and influenced during the hiring process.  You need to understand how things are viewed by your new boss; your new peers (and be warned, even when there aren't politics, there are always politics); and the people that work for you, and the people you will be working with.  To establish yourself, after showing that you are a careful listener, is to take actions - they speak far more louder then words.  Say what you will do, listen for feedback, agree or disagree, and do what you said you were going to do.  If you have to change your actions because you have new data - communicate that.  To drive results people have to believe what you say; they have to know they can trust you; and they have to understand how you can help them (and the company).  Communications - listening, and speaking - are key.  You wouldn't be there if you didn't have the qualifications - let your experience speak for itself in choosing good actions.  Don't be a yes person - be a person who listens, but takes action.

Just my two cents....good luck.

Starting a new C-suite role? Here's the quick guide to success:

Get the lay of the land: Understand the company, industry, and the reason for your role.
Build connections: Earn trust through listening, communication, and demonstrating your expertise.
Set clear targets: Align your goals with the company's and use data to track progress.
Drive changes: Find areas for improvement, build a strong team, and make data-driven decisions.
Stay visible: Communicate regularly, network, and keep learning to advocate for your vision.

Understand the organization, build relationships, define clear goals, talent assessment, build and establish the trust, focus on execution, embrace innovation and lead by example is what I can quickly think of.