I am not sure if premium processing is available for H4-EAD.
We are waiting for H4-EAD renewal result as the current one is about to expire in a month.
She will have to leave her job if she does not get approval before the last date.
There is no premium processing available for EAD application.
USCIS expedite request is the only option available.
https://www.truvisa.com/t/ead-expedite-request-with-uscis-no-premium-processing/368
As per my information, this request is NOT entertained if you just file it for the sake of doing it.
USCIS will seriously demand the documents in support of your claim like prove ‘Severe financial loss to company or person;’ or any othe rclaim that you make for expedite request.
If you can do it and convince USCIS, you should get the EAD faster than others.
One of my close friend filed this request in 2016 as he was in serious trouble. He sent all proofs and still USCIS denied it!
Then, he had used the services of congressman to send his request for checking on EAD and only after that, his request of expedition was approved.
If you want to go that way, find your local congressman, contact them and ask for helping you with your case.