Learn Spanish (Spain): Buscan a alguien que dirija el departamento. - They are looking for someone who manages the department.

To keep the same consonant sound! In Spanish, the letter 'g' sounds soft (like an English 'h') before 'e' or 'i', but hard (like in 'go') before 'a', 'o', or 'u'. To keep the soft sound of dirigir in the present subjunctive, the 'g' must change to a 'j' before the 'a' ending. If we wrote diriga, it would have a hard 'g' sound like "dee-ree-gah".

Why do we use the subjunctive (dirija) instead of the indicative (dirige) here?

Because the person they are looking for is indefinite or might not even exist. When we talk about "someone who" (alguien que) and we don't have a specific, known person in mind, Spanish uses the subjunctive to show that uncertainty.

Why is there an a before alguien?

This is the "personal a". Even though the specific person is unknown, alguien (someone) always refers to a person. In Spanish, when a person is the direct object of a verb (the one being looked for), you must put an a in front of them.

Why isn't there a word for "for" after Buscan?

The verb buscar means "to look for" all by itself. English speakers often want to add por or para after it, but in Spanish, the "for" is already built into the verb.