It's difficult because of the lens distortion. In *theory* since the sky just rotates about the pole, you could take the previous frame, duplicate it and rotate it around where the pole should be (in your case waaaay off to the right) - but that falls apart when there's lens distortion involved. It would get you close though, and you could tidy up the fake frame in Photoshop to get a reasonable match.
With minor lens distortion one route is to correct it away from every frame (in Camera Raw or Lightroom with the automatic profiler). Then you'd have perfectly circular trails and can just copy-and-rotate a frame here and there, and if necessary re-distort the entire composition back again when you're done repairing it. But your images look a long way from planar...
There's no truly automatic fix in After Effects since nothing is actually moving; you could have a stab with Pixel Motion Blur (precompose everything then apply it as an effect), but I doubt it'd work very well.
Thanks for the suggestions, I ended up creating small trails around the gaps in StarStaX then filled them up in PS. It's looking slightly better now, can't be bothered to fill in all the gaps though. I just thought there might be a feature that could do it like how StarStaX has a gap filling mode