Scrum teams should not have dependencies on other teams to release their changes.
So a good practise would be to let the Scrum to run the automation, maybe even integrate someone from your group into their team to make it truly cross functional.
Scrum is about enabling teams to self-organize towards a process that
maximizes their ability to frequently deliver working software and
adjust their process based on the feedback it generates from
stakeholders, customers and users. And anything that stands in the way
of self-organization should be removed or reduced.
read more here...
Now the team could create a PBI todo a release or just release after each user story is completed as my teams are doing.
Maybe it is harsh to hear, but silos should not exist in an Agile organisation, try and start eliminating them now! :)
Another way of doing this is to automate the whole process of running automated tests. Read the book about continuous delivery.