To receive support requests at an external email address (instead of your Zendesk Support email address), you need to forward email received at your external email address to an email address in your Zendesk account.
You configure email forwarding in your own email account, not in Zendesk Support. Exactly how this is done depends on the email provider you're using. A number of email providers allow you to create email forwarding rules so that you can select the incoming mail that should be forwarded to your Zendesk account.
After you set up forwarding, make sure you've added your external email address as a Zendesk Support address (see Adding support addresses for users to submit tickets). When you add your support address, your email will be verified and you'll know whether you've set up email forwarding properly.
Optionally, you can edit or create an SPF record to verify that Zendesk Support can send email on behalf of your email server (see Setting up SPF for Zendesk to send email on behalf of your email domain). You can also digitally sign the outbound email from Zendesk. See Digitally signing your email with DKIM or DMARC.
Follow the steps for your email provider to set up forwarding.