By "new style" do you mean a threadless fork? Yes you can but you will also need a new headset, stem and spacers along with the replacement fork. I assune your steerer diameter is 1" and that size is still easily available in threadless components.

You can still buy threaded forks so a direct replacement requiring only a new fork is a less expensive route. BTW, many bike shops will have a collection of take-off forks from owners who "upgraded" their older forks to threadless, carbon or both. Ask around and take your old fork to match the steerer diameter and length and fork blade length and you might get your replacement very inexpensively. The color can be matched with a rattle can or just paint it the currently fashionable flat black and everyone will think it's carbon.