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Does anyone know how you can hire a mathematician for a consultation? e.g. a PhD student in a certain area?

Sometimes I’m down a rabbit hole and I realize that the level of mathematics is becoming outside of my (undergrad-level) comfort zone and I often think it would be helpful to sit down with a mathematician for an hour and have a chat with someone expert in X (where X could be combinatorics, probability, statistics, linear algebra, etc...)

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It is generally not super difficult - most professors at universities have Masters and PhD level grad students, and more often than not, faculty are listed on the university websites.

Find a local university, look up their math (or whatever) department, and a simple email to one or more professors explaining what you want to do and that you're willing to pay will more than likely give you some leads if nothing else. Hell, you might even find that the professor's time is within your budget depending on the institution and their level of seniority.

Oh my god this, I once asked my old director of studies if he could put me in touch with the person who would be teaching a certain course I had not done very well in at University so I could hire them for tuition.

He offered to do it himself and when he told me his rate it was so low I was almost embarrassed.

Send them an email.

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