When copying large images into the copy paste buffer (eg 4000x3000pixels), it is possible to paste into an application like gimp, but not krita. If you paste, nothing happens. Pasting smaller images works, it just doesn't seem to handle large images in copy paste buffer.

Copy from where? Paste to where? Which OS, which version of Krita? What kind of hardware?

Using the krita 4.1.5 appimage, I've just done copy/paste between krita and GIMP of layers from a 4000 x 3000 image. There is a complication:

To copy from krita, you need to do right-click Copy Layer on a layer, then in GIMP you can paste it as a new layer or paste onto an existing layer.
From krita you can use Edit -> Copy provided that you do Select -> Select All first.

To copy from GIMP, you select a layer and do Edit -> Copy then in krita you need to do Edit -> Paste from the menu bar to have it pasted as a new layer.

If there is difficulty with a 4000 x 3000 image but not smaller images, does this suggest problems with the OS clipboard facility?

P.S. I've just copied a 5184 x 3456 image from an image viewer application to krita with no problem but it took six seconds.

4.1.5
Kubuntu 17.04
Copying from Mozilla to krita. Nothing pastes with large images, but does with smaller images.

The same large image will paste into gimp.

Make a bug report. Mention exactly which image you're trying to copy and paste.