The phrase "a more modern example" is correct and usable in written English.
You can use it when you want to provide an instance or illustration that is contemporary or recent in comparison to others.
Example: "To illustrate the evolution of technology, let me present a more modern example: the rise of smartphones."
Alternatives: "a recent example" or "a contemporary example".
But more modern examples are lacking.
There was already a Beaulieu Museum, but he decided to expand the motoring side of it with any significant item he could lay his hands on, from an ice-cream seller's tricycle to the world's first motorcycle, from ancient cars of long-deceased makes to more modern examples of British and other quality cars.
This type of bigotry has been (so far, and as far as I know) thankfully absent from the populist wave building out there -- but there have been plenty of more modern examples of such idiocy as well (such as Auschwitz photos of dead bodies waved at Tea Parties, for instance).
That makes the app sound similar in some ways to an older startup called Blippy, which once tried to build a social service around publicly shared purchases, or, for a more modern-day example, Venmo's social feed.
Yet a younger generation of conservative supporters who voted for Mrs. Merkel in 2005 did so because she wanted less state interference as well as a more modern Christian Democratic Party that, for example, made it easier for young mothers to return to work, and because she supported measures dealing with climate change.
The Libor scandal looks and smells like an old-fashioned financial fraud, but it also presents the latest example of a more modern phenomenon: the war against reality being waged with ferocity by special interests that profit from limited public awareness of what's actually taking place.
Both Esquire and Entertainment Weekly are examples of long-standing brands that have innovated to reflect a more modern approach to engaging readers.
