Learn Hardcore Korean: geu seonbaeneun got joreophaeseo yojeum aju bappa. - That senior is graduating soon, so she’s very busy these days.

Not exactly. 선배 means a senior in a shared context such as school, work, or an organization—someone who entered earlier than you or has more experience there.

So 그 선배 does not simply mean that older person. It means something more like:

that senior
that upperclassman
that more experienced person

A 선배 can even be younger than you in age, depending on the situation. The opposite word is 후배, meaning junior.

Why is there 는 after 선배 in 그 선배는?

는 is the topic marker. It marks 그 선배 as the topic of the sentence: as for that senior...

So:

그 선배는 = as for that senior
그 선배가 would feel more like identifying that person as the subject in a more neutral or contrastive way, depending on context

In this sentence, 는 feels natural because the speaker is talking about that person and then saying something about them: they are graduating soon, so they are very busy these days.

What does 그 mean here? Is it literally that?