Transfer old emails to a new Apple ID

Is the AppleID compromised or just the primary email address you use with it? If it is the email address itself that is compromised, get a free email and just change the primary email address of that AppleID to keep the AppleID active.

Change your Apple ID - Apple Support

If it is the AppleID that is compromised, have you tried changing the password and re-Secure it? If having difficulties, call Apple and they can help you secure a comprised AppleID - If you think your Apple ID has been compromised - Apple Support. If it is the iCloud email account associated with that AppleID that is compromised than simply re-securing the AppleID will take care of that iCloud email as well

You are welcome. If the accounts are iCloud accounts, try going to iCloud.com/Mail using a computer browser and sign in with the old ID. See if the emails are there. If so, select, and then click the below in the menu bar and forward it to the new address. You may be able to do multiple emails at once if you select the first email and while holding down the shift key, select the last email.

Device or computer? One option is to forward the emails to the active ID.