I'm a senior leader at my company and about to experience a major life change, my first child is arriving soon. What advice do you have for the change in my priorities and work/life balance that is to be expected? What can I do to manage my anxiety of not performing at the same "always on and available" level that I have historically?

First of all, congratulations!

Having a balance between your personal life and your work life isn’t different as the one you’re probable having right now. That is you must set priorities.

Let’s go first with your personal life, even though your first child will be arriving soon. Take time for yourself to do exercise during the week, that’ll help you take away the anxiety you might be having at that time. Understanding that a child is a full-time job, you and your partner will have to talk to each other constantly, to understand what has to be done and when. It is the same as if you had a project at the office. Your partner will rely on you and you will rely on your partner. Then, everything will go well.

At the office talk to your Manager, talk candidly and know in advance where the projects are right now. I trust that your manager is a humane leader that will understand and cut you some slack. If not, check on time and leave as well when your shift ends.

Work life balance is a grey area.  I think you will find that you have shifting priorities between family and career and will become more agile balancing the two. One piece of advice I got was “if you have to grind late, grind late at home.  At least you’re present in the home, together with your family”. Best of luck. 

Congratulations!!!
One would say, it's the most sustainable achievement one can ever reach.

I remember my situation. That's the perfect start for agility. Don't think about work-life balance, ensure that you have prepared to be agile. Your child and also your wife will need you and your time on short notice. This can be that also your wife is exhausted and you need to take over for giving her some minutes to recover or your child needs something urgently. Especially when it's the first child, you will visit the doctor more often, because you lack in experience what might be serious and what's not. Try to delegate more than you did before to free time for your family. maybe even set a target to have at least every day half the day without any meetings or other appointments. Prepare for not having slept sufficiently when arriving in the office and therefore ensure that you control your attitude and behavior.

in any case, all the effort will give you much more in return, even when you sometimes start to believe, it won't.

Congratulations! It is an adjustment and as others said, give yourself grace. You won’t be able to do it all at the same time. Take time to think about what you value and prioritize. As you return to work, review how your values align with how you are spending your time. Be intentional with your time, set boundaries, say no and look at it as an opportunity to have some of your HIPOs take on more, get exposures to other areas of the business. 
Be gentle on yourself. 

Give yourself grace. Lean on others to help and know that whatever stage you are in, it won't last long.