Can I stop the subscription discount from combining with other discounts? (Essential Subscriptions app)

There's no setting in the app for this. Whether a subscription discount can be used together with another discount depends on Shopify's discount combination rules and on how the other discount is set up.

For discounts you create in Shopify → Discounts, check the Combinations and Purchase type settings on each discount. Purchase type lets you choose whether a code works on one-time purchases, subscriptions or both. See Shopify Limitations for Subscriptions.