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 -->