I'm afraid it is not that easy.
The headset does not seem to match.
Your current bike's headset is straight, the new frame is tapered( top and bottom of different diameters).
A new fork would be best.
But there are adapters that exists to reduce the bottom diameter, and reuse your fork, but it may be clunky.
There is no indications of the bottom bracket of your current bike, but chances are it is BSA which is threaded and fairly standard on older bikes.
So you could keep the crankset, and the full transmission(rings, cassette, derailleurs, shifters, chain).
The rear wheel is probably 135mm wide, while this frame use the boost standard of 148mm.
So you'll need at least a new rear wheel.
The seatpost is probably wider on the new frame, and you probably would need a larger one.