If you can, don’t be afraid to run your automated tests in production. A production environment is a place where automated tests can give real value, especially after a release. Instant feedback on the success of a change in production could be worth a lot of money to your organisation.
As a minimum run automated smoke tests before and after a release in production, firstly, to baseline, and secondly, to assure nothing has broken after a release.
If you are limited by the data you can use or create during a test then just consider non transactional tests. Any way that you can speed up the feedback loop when a change has occurred is a bonus.
Obviously not all systems or organisations are conducive to this sort of strategy, so as a consideration when building a new system, it’s worth thinking about the ability to run automated tests in a live environment when designing a system.