Julie here from Shopify Support.
I managed to search for "LinkedIn" in the Shopify App Store and found a couple of options for you. Both Auto Post on Instagram, FB, TW and Instagram & Facebook Auto Post offer integrations with LinkedIn, allowing you to schedule and automate your social media posts.
These apps sync with your Shopify product catalog, making it easy to share your products across your social media channels. With these apps, you can also choose to automatically post on LinkedIn whenever you add a new product to Shopify, and you can even choose to automatically post products from specific collections. As their titles suggest, they also integrate with other social media platforms, like Facebook, Instagram, and Twitter.
I hope these apps offer exactly what you're looking for and I'd love to learn more about the types of posts you plan on sharing on LinkedIn!