When you say 'Header', do you mean the WordPress Admin Toolbar? If so, this is how you can achieve your goal:
Remove WordPress Admin Toolbar for all:
Head into your Child Theme's functions.php file and enter:
show_admin_bar( false );
This will remove the WordPress Admin Toolbar, on all Front End pages, for everyone.
Remove WordPress Admin Toolbar for selected users:
You can also remove the WordPress Admin Toolbar, for specific users only. If you would like to do this, one option is to enter the following code within the same functions.php:
if ( ! current_user_can( 'create_sites' ) ) {
show_admin_bar( false );
}
What the above code is saying:
Line 1: If current user can create sites on the network ...
Line 2: ... Show WordPress Admin Toolbar? False (ie ... No!)
Using this code as a template, you can modify it to remove the Toolbar, based on specific users.
To do this, head over to WordPress' Roles and Capabilities resource. Identify the relevant Role/Capability. For example, activate_plugins, update_core and delete_posts etc.
Replace the create_sites entry, with your desired Role/Capability. It is as simple as that.
Needless to say, if you change false to true, it will show the Admin Toolbar, for that Role/Capability. This may be useful, if you want to remove the Toolbar for all except for a handful of Roles :-)
Additional useful resource: https://codex.wordpress.org/Function_Reference/current_user_can