This is difficult English. Newspaper headlines and subheadings and TV log lines like this are often hard even for native speakers. Typically, you need an understanding of other aspects of a news story to grasp headlines, which are frequently shortened to just a bare minimum of words to save space (for bigger text) and to attract attention. The headline writer does not want you to understand everything from the headline: the goal is to intrigue you to find out more. Similarly with TV programme descriptions like this: the goal is to catch your interest. Then current catch-phrases or jargon (like "edgy") can be attached to signal that this is something you might like.
Translations into English ...
"Edgy" - current buzzword meaning "fashionable", or perhaps "tense", or perhaps "using modern film technique".
"Drama" - a play or film.
"Starring" - this introduces the name of one of the main actors.
"play-it-safe manager" - they made this up. A manager is a person in a business who has responsibility for others, or for some aspect of the business's activiites. or both. To "play it safe" is to avoid risky choices and do things as they are normally done - the opposite of "exciting", you might say.
So a "play-it-safe manager" would be a conservative, boring person who looks after some aspect of a business- or government function, or a charity, but in this case a business.
"Cash counting house" - I had no idea, and had to search. Really it means a bank vault, a place for storing gold and valuables. But the words don't tell you that.
2 This is for a long-running BBC show called Question Time. In each episode a host, or "chair", or "chairman", or "chairwoman" is joined by several guests - "a panel of guests". The host was often David Dimbleby, though more recently Fiona Bruce has taken over. The panel usually has people from all the main politcal parties and perhaps also a "celebrity" - someone famous for something - and perhaps a specialist in a particular topic.