When it comes to live listening I usually start talking, as a warmer for the class, about how was my last weekend, last vacations, or so, but in such a way that ss are exposed and have to use as well the vocabulary or grammar seen the previous lesson. For instance, if we studied present perfect the previous lesson, in the current lesson I start with something like: what are you planning for your next vacations? is there a place that you've been to and would like to return? this requires a little bit of preparation because you need to ask the right questions so that ss answer using the grammar or vocabulary that you want them to use.
I belive live listening is quite useful since recordings at times are not that clear, regardless the fact that they're in English. Even with L1 recordings, at times you might struggle to identify a word.