You can change your email address on Tumblr if you want to close the old address or just want to receive notifications on another address. You need to have access to the new email address in order to confirm it. After you confirm, you can safely close the old email account.
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Log in to your Tumblr account, click the Account icon in the top right corner, and select Settings from the menu to open the Account Settings page.
Click the Edit button next to your email address in the Email section — this appears as a pencil icon — to edit the address.
Type the new email address into the first field and then type the Tumblr password into the second field. Ensure the email address is correct and click the Save button to apply the changes.
Open the email you receive from Tumblr on the new email address and click the Verify Email Address button or hyperlink to verify the address.