You have a learning curve to go through, for sure.
Your VP will always be busy, this is common. Your VP expects you to manage the team on a daily basis so he can attend his hundred more responsibilities.
Make sure to schedule a weekly meeting with him. You will have to be succint in such meetings, give a quick summary of the current state of the projects, and anything you require from him.
For how much busy a VP can be, he won't have much trouble (hopefully) with having a weekly meeting with you, as he can lock down his calendar for that time and this gives him a more organised schedule.
Regarding the day to day management, you will have to find your way to resolve most of the issues without having to require the VP. For that we miss a lot of context on what is that the VP is giving you that you can't find on your own.
Either way, if the issue you or your subordinates encounter certainly requires VP intervention, you will have to decide whether the issue is urgent or it can wait until the next weekly meeting to be addressed.
Finally, if it's causing you stress, think what is the cause of that stress and try to address it. It is normal to be uncomfortable during a new stage in your professional career, with new role and responsibilities, but if this stress continues over time, try to find the root cause or get some professional advice.
Best of luck in your new stage.