What is the right term for students admitted to the school in previous years, if you are also a student? Do you call them "elder students"?

x "year(s) ahead of" me
y "year(s) behind" me

He is fond of casually dropping the names of his drama school contemporaries. Ewan McGregor, Joseph Fiennes ('We would potter next door to see Ralph playing leads at the RSC'), and more long-term friends such as Dominic West, whom he knows from his Eton days. 'Dom was a couple of years ahead of me,' Lewis recalls.

from The Telegraph

President Obama was four years ahead of me at Harvard law school....

quoted in The Atlantic

That reminds me: Lee Harvey Oswald, a year or two behind me in school, lived in Covington in those days.

from the New York Times

Prince Harry had started at Sandhurst in May 2005 and was a year ahead of his older brother.

from the Evening Standard

variant:

My favorite Stanford summer was 1979, when a woman engineer in the class ahead of me helped me get a summer job at Chase Manhattan Bank in NYC.

Stanford University website

In the United States, we would say the following:

• Freshmen (first year)
• Sophomore (second year)
• Junior (third year)
• Senior (fourth year)

The following terms work both for high school and college, both of which are typically four years. In other English speaking countries, they would usually just say first year, second year, etc. Even in some American Universities, this is becoming more common as fewer students complete their degrees in four years as is traditional. Personally, I went to a school where the typical degree took five years, so we used the term middler to describe a third year student, while junior and senior described a fourth and fifth year respectively.

Additionally, for simply contrasting two students of different years, you could say lowerclassman and upperclassman. The former refers to a first or second year student, while the later refers to a third or fourth year student.

If I were saying that another student helped me with something, I wouldn't consider it important to mention whether that student was of a higher year, a lower year, or the same year. Maybe this could be considered a bit of a cultural difference.

If, for some reason, I did consider it important to identify the year of the student who helped me, I'd be more likely to do it by identifying the grade level (e.g. "a tenth-grader helped me") or by using the terms "freshman", "sophomore", "junior", or "senior" if those terms are applicable. But I still generally wouldn't emphasize the relationship between that student's year and my own.

In a pinch, I could say something like "an older student" or "a more senior student", but those strike me as phrases characteristic of more formal or clinical speech. It's just not something I would include without a strong reason to do so.

There are often regional names for students of specific years (the most common in the United States being freshman, sophomore, junior, and senior for 1st, 2nd, 3rd, and 4th year of a four year program, respectively). For a more general term, I would typically say, "A more senior student" or "A more advanced student".