While researching brands that use traditional advertising in a new medium, the most prominent example I could find was online advertising. Firstly, I think it's fair to say that all, if not the majority, of brands have a website. Every company that is a traditional advertising media (for example: The Ottawa Citizen for newspaper, CTV for television, or Chatelaine for magazines) has an equivalent of their newspaper, TV station, or magazine online. That alone is putting traditional media in a new medium.
As far as advertising goes, these sites offer ad space to companies that advertise with them through the traditional media. Most of these ads are taken from their original form (print or commercials) and transferred to a new, digital medium.
At the beginning, when online advertising was first getting popular, I remember that the banner ads on websites were so simple and would just flash from one picture to another. Now, online ads can actually be a mini commercial. Here's an example.
When you click on the different tabs in this website, you will see that most of their advertisers are making mini commercials with their spots.
It seems that as time progresses, traditional medias are starting to integrate with each other. Just in this one example we have a two traditional medias (magazine, and television—the online ad is a copy of their TV spots), and we have two new medias (website and online advertising) all meshed into one. This goes to show that it's getting harder to get the attention of consumers and only by integrating a number of media can we actually get through to them..