The correct answer is who works at that desk.
There are two types of clauses: subordinate and independent. Independent clauses, as the name itself suggests, are complete and can exist on their own. In the example above, the independent clause would be The woman is absent today.
On the other hand, subordinate clauses are incomplete thoughts - they need to be supplemented by other words in order to be grammatically correct. In the example above, if you just write the clause who works at that desk and leave it at that, it is definitely grammatically incorrect. But, if you write that entire sentence, then it will make sense.