Without knowing the template, that seems to me to be a fixed menu block, and probably using CSS padding values which means it would always be visible even when empty. If this is the case you could do some CSS override (unless it’s a custom template in which case you could edit the CSS files).
Alternatively it could be removed from the header.php files.
With CSS. But we need to see the site to be able to tell you what specific code to use. That said, that gap probably shouldn’t be there – I’m guessing something is in the wrong place or has the wrong dimensions.
Without knowing the template, that seems to me to be a fixed menu block, and probably using CSS padding values which means it would always be visible even when empty. If this is the case you could do some CSS override (unless it’s a custom template in which case you could edit the CSS files).
Alternatively it could be removed from the header.php files.
With CSS. But we need to see the site to be able to tell you what specific code to use. That said, that gap probably shouldn’t be there – I’m guessing something is in the wrong place or has the wrong dimensions.