Since scripts registered by Shopify apps' are loaded once the page is loaded successfully, You can add following line of code in your theme.liquid before ending </head> tag:
<!-- ULTIMATE Cart Drawer --> <script type="text/javascript" async="async" src="https://cdn.shopify.com/s/files/1/0537/1265/0427/t/2/assets/ultimate-cart-drawer___app.js?shop={{shop.permanent_domain}}&t={{ 'now' | date: "%Y%m%d-%H"}}-01"></script> <!-- /ULTIMATE Cart Drawer -->