What's the one piece of advice you would give to someone starting in a VP of Product role for the first time?

I think this depends on whether you've been a people manager (e.g at the Director or Head level) previously. 

If you're a fist time people manager, it can be a challenging transition. The biggest trap people fall into is not delegating aggressively enough. You got to where you were by being a rockstar PM. There will be many, many situations where one of your employees is struggling with something and you will be so tempted to do it yourself. It will way less work than coaching them through it and the results will likely be better. Avoid it at all costs, you are going to disempower your team and deprive them of the opportunity to learn and grow. 

If you already know how to avoid that trap, I would fall back on Fred Wilson's advice for CEOs. It applies to VP of Products, too. He says a CEO should only do three things - (1) set the high level strategy (2) make sure there's money in the bank and (3) recruit and develop a world class team. Delegate everything else. As a new VPP, you're probably best equipped to do (1), you've been thinking strategically your whole PM career, now you just need to do it at the portfolio level. For (2), you may or may not already be good at this. Think of your product as a business and double down on GTM - this is a blind spot for many of your IC PMs. and (3) is the most important of all. Get really good at hiring and inspiring - building a world class product org is the most important thing you can do for your company.