Do I need to buy a new headset or is there some sort of an adaptor I can get?

Hope do one. About £8

will that fit any make of headset?

Yes it will. It presses onto your fork to make the base of the steerer effectively 1.5, then fit the crown race to that.

I’ve got one you can have for a fiver?

You need a different adapter (or a new bearing) depending on the bottom chamfer angles on the lower bearing. Some are 45 degrees and some are 36 degrees. There may even be others. I think hope use 45 degree and I know FSA use 36 degree lower chamfer bearings. However, adaptors are available for both and if you get the wrong one you can always swap the bearings as I think they all have 45 degree upper chamfer.

The Hope adaptor is square edged to take any crown race, it isn’t tapered & a crown race in its own right.