1. Log into cPanel
2. Under the ‘Email’ section, click ‘Email Accounts’.
3. Select ‘Manage’ to the right of the account you want to update:
4. Enter your new password in the ‘New Password’ section:
You can then scroll down and click "Update Email Settings":

Your new password will now be in effect for the desired email account.
Please note
If you have a mail client (outlook, iMail etc) that has the old password will continue to retry with this until updated. This can lead to the IP attempting to connect being blocked for incorrect mail login attempts.
Its recommended to update the mail client password ASAP after changing.