Need to Hide the Top Search box on a Classic Site

I have a Modern Team site in SharePoint online and it has a classic subsite.  I noticed that the classic subset has a top search box in the Sharepoint ribbon at the very top.  I am not talking about the search box usually found at the top right of a classic site.  I need to find a way to remove or hide the Search box in the ribbon for at least the subset.  If I have to remove or hide it from the whole site, that is fine too.  Would greatly appreciate some help on this.  Just for clarification, I have attached a screenshot of the search box that I am referring to.

Thank you!