What would you do, if you are in a situation where in you are requesting for a certain input from a very senior person in the management and he is not replying back to your emails, phone calls etc. And this input is crucial for you to meet a deadline.

to know the right way

Convey to the right chanel

I would start with emails, if that does not work, I would personally try to catch the supervisor and make sure I explain the situation or possible get the right advice I seek.

I will send an email to the senior person and will take follow-up on that email. If it doesn't work. I will catch the superior and make sure I explain the situation or possible get the right advise I seek. If the situation get worst before I get reply or catch the superior, I will convey to the right channel.

Escalate it through the right channel.

I personally meet and ask the reason

Personally meet to senior and communicating them to resolve issues