While Alex’s method works, After Effects doesn’t support Tape Names, so you will effectively be losing all of that going to AE, additionally you’ll probably lose other metadata associated with the clips. This is important if you ever need to have multiple users using the same clips, or need to go into an online and offline workflow.
Why not just subclip in Premiere Pro, select all of the cilps in the project panel, and export your subclips from there. (unless i missed something in one of the responses)