What does the expression "as is their want" mean?

You probably misheard this: ‘As is their wont,’ which approximately means ‘As is their custom.’

To say that something ‘is/was someone’s wont’ is fairly idiomatic. The definition I linked to provides this example: He awoke at the crack of dawn, as was his wont. And similarly the OED provides this example from Shakespeare: ‘Tis not his wont to be the hindmost man.

Not to be confused with won’t, as from will not.

Never heard of it, can you use it in a sentence?

What @absalom said, though I’d say that ‘wont’ is more like a tendency than a custom.

@Nullo

Yes, ‘tendency’ actually is probably better. Or even ‘habit.’

I would go with “habit” too.

I would have given the same answer as @absalom. This is an old expression and rather literary.

Another use (this one an adjective, not noun as in the original question) is “to be wont to,” meaning to be used to or accustomed to. This expression is about custom or habit, not tendency. Example:

She was wont to begin her breakfast with lavish helpings of jam on toast.

It means she was used to doing that—it was her routine.

Sometime you see “wont’ in another form, namely, “wonted.” Example:

I found them sunning themselves in their wonted place at the edge of the cliff overlooking the long valley.

It means their usual or customary place. This too is much more likely to turn up in literature than in conversation.

“Sometime” (above) should be “Sometimes.”

Isn’t spell check nasty? You never knew you had the wrong word, when you ran it through spell-check, as has been your wont.