Virginia is an at will state. If there is a job contract, that states "21 days notice" is required.

Does this hold weight in Virginia? Can this "at will" state be overridden with a contract or not?

Simple question, need a simple answer :)

Yes, the contract negates the at-will status. Contracts are legally binding.

Does the contract contain any provisions wherein certain circumstances may permit a separation regardless of the 21-day provision.

I am thinking some sort of "just cause" provision. For instance, I find it difficult to believe the employer would sign a contract that requires them to give 21-day notice to an employee who embezzles from them????

Their side of the contract requires them to give 14 days notice, or 7 days notice in a few select circumstances.

Aside from that, no notable provisions.

If an employee who is under contract is found to be guilty of some impropriety against the employer, they can always "suspend" the employee for the full notice period or put the employee "on administrative leave" pending termination.

Question here - what consequences could I face for violating the leave agreement?

What "leave" agreement? Do you mean notice? If there is a requirement in the contract, the contract should also state what the consequences are of breaching it. Theoretically, you could be sued.

So, to be clear, the contract mandates that you provide your employer a 21-day notice should you resigne, correct?

As Patty referenced, does any part of the contract state what if any penalties exist if you fail to do so?

It does not list any penalties for violation.

Then you will need to show the agreement to a local attorney to tell what, if anything, the employer can do if you violate the agreement. We cannot comment on an agreement we have not read.