Below is some javascript that will hopefully append a new link to the top right hand side of your current logo. You will need to add this script to your theme.
I’ve added comments to explain what I’ve done but feel free to ask me any questions if it’s not clear.
<script>
// Create a div element with class secondary-logo which will contain the secondary link inside.
var secondary_logo_link = document.createElement('div');
secondary_logo_link.className="secondary-logo";
// Add the secondary link (replace https://www.google.com with your desired url) to the new container element. Also adding custom CSS styling to help position/size the new element correctly.
secondary_logo_link.innerHTML = '<a href="https://www.google.com"></a><style>.logo{ position:relative; }.secondary-logo{position: absolute; top: 0; right: 0; width: 27%; height: 100%; z-index: 1;}.secondary-logo a{height: 100%; width: 100%;}</style>';
//Finally append the new secondary-logo element to both occurances of the logo (header and sticky).
document.getElementsByClassName('logo')[0].appendChild(secondary_logo_link.cloneNode(true));
document.getElementsByClassName('logo')[1].appendChild(secondary_logo_link.cloneNode(true));
</script>