You don’t need the services of the mail any longer or it’s probably outdated then take the below steps to delete your gmail account.

Step 1

Sign in to your gmail account at gmail.com on the web.

Step 2

Click on the account preferences page (this can be seen at the top right corner of your account) just click on your avatar or your picture (or profile) and a drop down menu will appear which would consists of log out button and others, there you would find the account settings.

Step 3

Click Delete products. You may need to sign in to your account again.

Step 4

Click the delete button that is close to gmail.

Step 5

Follow the instructions on the screen, then choose Remove Gmail.

more at
https://encyclohow.com/2017/09/20/how-to-delete-your-gmail-account/

very informative,
cc lalasticlala