10 ways to get the attention of a producer/director of a tv show?
make a video with clips of the show and send it to the producers/ show runner. How to know who to send it ? This might take some creativity. easiest way would be to buy an email list for TV show runners / producers. Study the credits. Especially whoever is in charge of music. Google them and see if they have any social media. You can DM/ Tag or post on their feed. If we are all 7 degrees of Kevin Bacon then you probably know someone who knows a guy who banged a girl that eventually ends up with the right contact. Hope thast helps.