Make a comp and decide you need a bit of a clip from the Editor timeline in it - for a Transition between two layers for example.
Cut the second clip section, copy it, go into the first comp and select Paste - which is not greyed out, so should work. Nothing happens.
Instead, create a comp with the second clip, go into that, copy or cut the clip, go to the first comp paste it there. It works this time. Then go to the Media Bin and delete the redundant second comp, as you're not using any part of it; you got the clip you wanted.
It seems like it shouldn't be necessary to do this if the original 'Paste' worked properly.