This would be a simple question .
To migrate my Google Analytics Code to Google Tag Manager , do I just only activate GTM, Leave for a couple of weeks Google Code in Header and then deleted???
To migrate, I recommend adding the Google Tag Manager container to your website, then test that the pageview tag for Google Analytics is working in preview and debug mode.
Once you are happy that this is functioning correctly, you can remove the Google Analytics container and activate the pageview tag in Google Tag Manager.
If you are concerned about current event tracking on the site, you can take a number of other steps to ensure safe migration such as setting up a temporary test property. See this article for more details.