Wise (formerly TransferWise) likes to keep things simple. Visitors to its press page are hit with the logos of previous earned media – the BBC, the FT, the Guardian, This Is Money – as well as a teaser quote of their recent coverage.
From there, they have two crystal clear options: contact the press team or download the media kit.
By keeping things clean and direct, Wise removes a lot of the decision-making stress from the reader, and likely shortens the time it takes for an interested journalist to get in touch. Similar to Lyft's example, the call to action is as clear as can be.
The teaser of their previous earned media also helps demonstrate the sort of content they would likely be happy to provide – in this case, an interview with the founders. This again makes life easier for the journalist by suggesting a format (interview) as well as showing what angles have already been covered. Another way to achieve this is to include your most important recent press releases within your press kit or media center (another point for integrating the two with your newsroom!).