There are not many examples of this. I know because I did some research. I’m not going to claim that I did exhaustive research — I had plenty of energy left by the time I was done searching Pro-Football-Reference for a little while — but I went through plenty of motions to get here.
You’ll see the results of some of those motions at the bottom of the article in notes, but here’s the most relevant find to the premise at hand.
In the 2000 NFL Draft, the New York Jets held picks 12 and 13 and neither of those picks were their original first rounder.