There are some regulated business sectors which require “old-fashioned” software testing, for due diligence reasons, especially a need to have cast-iron audit trails. Medical systems is one such area; finance is another. This usually involves manual script execution with detailed lists of test results achieved. That’s just the way it is.
That isn’t to say that more modern test techniques - exploratory testing in particular - can’t be used as well. Even if your organisation doesn’t work on an agile basis and so you are waiting for new releases to be thrown “over the wall”, that doesn’t mean that you can’t do some exploratory work on earlier versions, or on versions with known bugs that you can avoid to see what else is, or isn’t working, and how well. Finding bugs that are off the ‘happy path’ but still have a better-than-medium risk of occurring in deployment will add value to the product (in avoiding rework later) and demonstrate the value of more flexible testing approaches.