Do discounts from my Shopify store apply to subscription automatically?
This can depend on how you are discounting your products. Shopify's automatic discounts and Buy X Get Y discounts are not compatible with subscriptions and won't be applied. However, if you discount your products by changing the product price directly in the Shopify admin product page, that new price will be reflected on the storefront allowing new customers to subscribe.
It's important to note that changing the product price does not affect existing subscribers. Existing subscribers will continue to receive the price they originally agreed to at purchase.
Read more about using Shopify discounts codes with subscriptions here: https://support.boldcommerce.com/hc/en-us/articles/11369207621012-Discount-Codes-for-Subscriptions-for-Shopify-Checkout