Okay from what I have seen going by canonical art and fandom, no.
So canonically? We can go off ESO which I believe has chimer in it and all the ones I have seen have your default sclera.
But if you wanna actually have fun with it?
BUT adding in an educated guess, lore wise it makes sense if you want a sources for how they might look to look at the Altmer, Alyids, Derenni and Osimer.
Chimer like those groups split from the first era or merithic era Altmer. We know the altmer in lore are the race least likely to have "changed" and I believe we dont see any unique sclera within them.
Same with the Derenni and Osimer. If you wanna be super nitpicking, the Osimer and Chimer are "changed" by the same event and depending on your preferences for what story you like.
The elves that do seem to have sclera changes are Dunmer and Bosmer. Bosmer out of all of the races might be one of the rare few we can argue is actual evolution, they too are an Altmer separation group but unlike the others seem to have the least interference. Y'ifree specifically prohibited changing their forms outside of true emergencies so we have less daedric meddling. Their bodies are more likely a change of adaptive body plans over time fitting their lifestyle as hunters in a heavily forested arbordial lifestyle.
Dunmer are a bit more boring but next to Osimer have the most drastic body change. They are changed specifically because of Daedric (Azura) meddling. That is straight up Azura installing custom content onto them.
So for Sclera? Nah. Those fuckers got nada.
"Des why did you write all of this"
Im sleep deprived and trying to stay awake!
So here's the super fun bit! Because of lore gaps you can actually infer a whole bunch of stuff and there are some really cool ass headcanons out there that you can grab from, I actually used some of these for my own chimer oc!
- Based on 6th house artwork and how they are in morrowind, you can actually argue they might be dead chimer and not dunmer! That means we can yoink out the dual ideas of at least some chimer having red irises AND a third eye! These might be house dagoth genetic traits but go wild.
- Vivec! (Fucking Vivec) He gives us the argument that heteochromia was a more common trait within the population. Not all heteochromia is two clean split iris colours too btw so plenty of potential there.
- Nerevar is almost always depicted as having blue eyes
-You want them to have completely black sclera or eyes we see in other races? Hey fun fact, lore wise race is determined by the mother BUT a father will pass on traits. So a Nord Father with a Bosmer child might have their facial traits or body build reflected in their child. Your character had completely black eyes? Grandpa was a bosmer
