I'm being stalked and the stalker is a hacker. If he gets my new email address can he get my IP address from it?
The question was answered in the comments and summarized here in case someone else comes searching with similar questions.
The email address on its own won't reveal IP address of Sender.
One needs to have access to email sent from given address and email service provider has added to headers sender's IP address. One should note that many service providers do not add IP address of sender. Further, this applies to only emails sent out from a fixed line connections like Broadband or Leased Line etc. Emails sent out of mobile phone connections usually carry the service providers IP address and location information is out of reach for most people.
Edit: As @scott commented one can always find the incoming mail server IP address for the email address in question. If the given domain is hosted on mail services like GSuite, the IP address of incoming mail server will reveal very little or nothing.