Can my partner come with me on a student visa?

An unmarried partner cannot be a dependent on your D-4. She needs her own basis to stay. That is the direct answer, but there are several workable routes.

Why: the dependent visa (F-3) covers legally recognised spouses and minor children of certain visa holders. Korea does not recognise unmarried partnerships for immigration purposes, and the F-3 is in any case not available to D-4 holders in most circumstances — student dependants are generally only permitted for degree-level (D-2) students, and even then it is restricted.

So the realistic options for her, in rough order of how commonly students use them:

1. Her own D-4. She enrols in a language program too. This is by far the most common solution among couples, and it is often cheaper than people expect because you share housing. It also means she has structure and a social circle rather than waiting for you all day.

2. Working holiday visa (H-1). Available to many nationalities including Spain, usually with an age limit around 30 and a once-in-a-lifetime restriction. One year, work permitted, very few conditions. If she qualifies, this is the most flexible option available.

3. Her own employment or a language-teaching visa if she is eligible.

4. Tourist entry, which for Spanish nationals is 90 days visa-free. Not extendable for this purpose, and repeated back-to-back entries to effectively live in Korea will get her refused at the border. It works for a visit, not for a stay.

What does not work: entering as a tourist and switching to a long-term status from inside Korea without a qualifying basis, or repeated border runs. Immigration sees the pattern and acts on it.

On the practical side: two D-4 students sharing a one-room is a genuinely common arrangement and works out cheaper per person than one student alone. If she has any interest in Korean at all, that is the path with the fewest complications.