The tag for NewRelic consists of 2 parts: one for the head and one in the body. How can I publish this tags using Google Tag Manager?
Google Tag Manager does not support two part tags:
Certain tags with snippets in the header and the footer. While you can use event based rules on gtm.load to fire some of these tags (see the developer documentation), two-part tags usually imply some need for synchronously loading tags.
It sounds like you are out of luck in regards to this particular tag.