Forwarding your emails to your Office 365 email account depends on the options available in your existing email service. (What is email forwarding?)
If your email service supports email forwarding, there's likely a settings or properties option that lets you set up email forwarding. Select that option and specify your Office 365 email address as the address you want to forward your email messages.
If you can't find a forward email setting, ask your current email service provider to forward your email to your new email account, also known as mail relay.
Here's some tips from other email service providers: