Welcome to the Atlassian Community!
Trello now uses "Atlassian Accounts" as its user directory, so when you log into it, you are using (one of) your Atlassian accounts to get it. That's the same as the Community here.
Assuming your account is not "managed" (your organisation owns it, not you), then you can change the email address on it to any email address you can get email on (it will need you to confirm the validity of the new email and prove it is yours, so it will send you an email to do that)
Go to start.atlassian.com and log in with the account you use for Trello. Click on your profile icon at the top right, and go to manage preferences, then "profile and visibility" (which is usually a default landing place, so you might not need to click it). At the bottom of there, you can edit your email address.
Note - if your account is owned by your organisation, you will not be able to do that, they will need to update it for you.
You may be warned that it can take up to a week for the change to reach all Atlassian systems, but that's mainly for some of the partner-related systems, it's a couple of days for non-partner related accounts. You might have a couple of days of Atlassian emails arriving apparently randomly on both old and new. But for the main Cloud systems, including Trello, I've not seen it take more than "go make a cup of tea, feed the cat, and open the post"
You need to do this as soon as possible, while you still have access to the old email address and the new one.
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