Hello there!
Basically there are no High elf Spellbreakers by default, and first Spellbreakers were made by Kael’thas, when they already became Blood elves, and later they joined the Horde, while High elves remained with Alliance. At first look the answer is no.
But! That doesn’t deny the possibility to become one. I can think of several ways:
1- Overall your High Elf Character being specialized in Anti-magic and Spellbreaking, similar to that, but not of actual ones.
2- In some way, learnt from Blood elves. How? I can think of Neutral blood elves, like Scryers. Maybe your high elf is a Son of Lothar, and ventured to Shattrath and worked with Sha’tar and Scryers, and in some way, learnt to be a Spellbreaker. Namely working with them as Shattered Sun Offensive.
2.5- From void elves whom were blood elf Spellbreakers not long ago!
3- Another hard and unlikely is learning from the Nightborne, as they also have Spellbreakers, even different from Blood elves. It would be complicated that how they learnt from one, perhaps was before them joining the Horde, like during Legion?
4 & 5- Basically same, but from different sources, your High elf could’ve found a book or codex, either related to the Nightborne and Blood elves, and learnt through it.
6- Since Nightborne were Highborne not long ago and aren’t much different, and also have Spellbreakers, then i strongly assume Highborne also have Spellbreakers, or specializes in the arts of Spellbreaking. And your high elf could’ve learnt from one, maybe? Although this is a bit in headcanon route.
Perhaps you can somehow combine these ways to make one, although some people may misjudge at first, so i would suggest to not put “Spellbreaker” into your profile, so you don’t meet mis-judgement.
Sorry it became too long, and good luck!