Do you mean that you have apps (automations) set up with an existing button and just want to use this "new" button for the same purpsoes? If so, the above suggestions are apps that could create such automations in the first place, but it sounds like you already have something set up. To make it do what you want (if this is indeed what you want), you could just add this new button as another device to that existing app. How you do this will depend on that app, but Button Controller lets you choose multiple buttons to "trigger" the automation, so that would definitely work (or, as suggested above, is a good place to start creating such an automation for any button if you didn't already have something).
An alternative (if you're using 2.2.6 or later or using a button driver that implements this regardless of version), you could just write a rule that calls the
push() command on your "original" button device in response to a
pushed event on the new button. This is basically a way to create a virtual/digital button event that should wake/trigger all the same apps (rules, etc.) as a real/physical event without you needing to modify each of those to add one.