Hi @AdamDenham-2244,
You can attach app services to vnets in other subscriptions. When configuring VNET integration for an app service, you will notice in the portal you have the option to select which subscription the VNET you're integrating the app service with is in.
Since you stated you used a template, it's possible the VNET resource could be referenced by the subscription GUID, but I'm not completely sure on that aspect.
Regards,
Ryan