As an ex DeHavilland employee I'll admit I'm a bit biased, but I'd say there isn't really a "direct" replacement so far. Two reasons:
The Beaver was designed in Canada around a bush operator survey. Outside Canada (and to a smaller extent Alaska), "bush operation" generally means remote land operations into dirt strips. In Canada, "bush operation" meant almost exclusively seaplane operations, (and to a lesser extent ski operations in winter). The survey provided the Dehavilland Canada designers with a wish list of features provided by seaplane operators running Norsemans and the like (sadly, helicopters and gravel strips to provide land plane access remote areas have replaced most seaplane use as basic transportation, and today most seaplane operations in Canada and Alaska support the tourist trade).
So, unlike its modern contemporaries, it is specifically designed to operate on floats, and is optimized for being serviced and loaded from a dock. The fuel tanks in the belly, the placement and shape of the main doors, the battery location, etc. Easy to load, easy to service from a dock. The Beaver's modern contemporaries aren't optimized for float operations quite the same way so the "fit" isn't quite as good for a seaplane operator. On the flying side, the very long wings and full span slotted flaps (the ailerons droop with the flaps) allows it haul loads out of very small lakes, with a decent rate of climb.
The other big reason is the engine. The R-985 is one of the only large piston engines over 400 hp that is still commercially viable, that is, it's still feasible to keep running reliably in a commercial operation. A piston engine is far cheaper to operate than a turbine. Bush operators operate on very thin margins and direct operating costs have a direct impact on viability of an operation, so turbines are out of reach for most.
With the Petersen Mogas STC you can run an R-985 on aviation automotive fuel (Mogas) (like all 80 octane engines it's much happier on Mogas than 100LL), and in Canada at least some bush operators do this (the operator I worked for in the early 90s switched to Mogas when the supply of 80 octane in Canada dried up - 80 was still in production in Canada for some time after it disappeared in the US in the 1980s).
Add in the overall reliability of the design and ease of repair, and there you go.
The Beaver is kind of a single engine version of the DC-3. Its combination of features came together so well that after nearly 75 years, it's still the best choice for commercial seaplane operators to use as a business tool to make money. On top of that, it benefited from a large military order by the US Army that took roughly half of total production, 970 units, which has kept up the supply of used aircraft to keep prices in check (the story of the Army's adoption of the Beaver followed a trip to Alaska in the company demonstrator to take some generals fishing, and included a bizarre flyoff against a range of ill-suited contemporaries after US manufacturers complained about foreign sourcing - get the book the DeHavilland Canada Story for an interesting read).