If the headtube on the frame was sized for a 1-1/8" headset but the bike came with a 1" steerer fork, the shim (or, more properly, reducer) would have allowed a 1" headset to be installed. If you don't want to replace the fork, you still need a 1" headset. If you are willing to replace then fork, you will have to measure the frame's headtube inside diameter after removing the reducer to be certain it was correctly sized for a 1-1/8" headset.

BTW, 1" threadless headsets aren't that common anymore but the Cane Creek 40 is available in that format. I just installed one on an old Litespeed frame.