Learn Russian: У нас есть новая вакансия, хотя мы недавно наняли сотрудника. - We have a new vacancy, although we recently hired an employee.

Хотя means "although" or "even though." It connects two contrasting ideas. Notice that in Russian, you must always put a comma before хотя, and it doesn't force any special word order or verb tense in the clause that follows it.

Why does сотрудник (employee) change to сотрудника at the end of the sentence?

It is the direct object of the verb наняли (hired), so it takes the accusative case. Because an employee is a living person (an animate noun), its masculine accusative ending matches the genitive ending, adding -а.

Why is the perfective verb наняли used here instead of an imperfective verb?

We use the perfective aspect because the hiring is a single, completed action with a clear result. We successfully finished hiring someone, which makes the fact that we have a new vacancy surprising!

As a quick reminder, why do we say У нас есть for "We have"?

This is the standard Russian way to show possession. Instead of using a direct verb for "to have," Russian uses У + [Genitive case, here нас] + есть (is). It literally means "By us there is a new vacancy."