When applying a texture pack to a existing world and then uploading the world to the realm. When joining the realm the texture pack does not load and the default textures remain. In this case it is the Chroma Hills texture pack. I have tried to upload on both my PC copy and Xbox one copy of the game with the same results.
The world use to have the texture pack before 1.6 but there was an issue with it so I removed the texture pack until the update to it was released around the time 1.6.1 came out.
I have done a number of searches and did not find a reference to this issue. There is also a Reddit post on this issue where a couple other folks were having the same issue. https://www.reddit.com/r/MCPE/comments/9g4nvw/help_texture_pack_not_working_on_realms_xb1/e667vkw/?context=3
I do not have a screen shot of this issue due to the nature of the problem. If a world download is needed let me know the current world is 70MB.