What do you call something that is not first in a sequence?

Solution 1:

noninitial

The word has been used in literature on English grammar and other fields. Google books records, for instance:

"On the one hand, the finite verbal category seeks a noninitial position ..." -Géraldine Legendre, Jane Grimshaw, Sten Vikner: Optimality-Theoretic Syntax, 2001, p264.

"Noninitial stress may be found on any syllable of the word, and may or may not co-occur with initial stress." -Jean Ormsbee Charney: A grammar of Comanche, 1993, p41.

"Consequently, even for monosyllable words, CS and LEC factors can be distributed over different word positions in several ways: CS can be word initial (e.g., “quick”) or noninitial ..." -Peter Howell, Recovery from Stuttering, 1947, p155.

Wiktionary defines noninitial as Not initial.

Solution 2:

"This element is __ in this sequence."

While not a single word, surely this is the most logical alternative:

"This element is "after the first element" in this sequence."

I think subsequent would be grammatically correct, albeit somewhat of an awkward sounding sentence.

"This element is subsequent in this sequence."

Solution 3:

You should look into things like later, non-initial, non-starting, postponed, and postpositive.

However, I do not think you should use a single word here. Use a clear and simple multiword construct instead. “Elements after the first” is just fine, and indeed preferable.