Before I start, I want to say that personally I'm okay with it as is. I'll be happy to help out PUBs regardless of whether there are additional rewards or not.
I would like to recommend that after someone has already claimed the reward for HoL that week, there is some small reward for subsequent completions of HoL.
My concern here is that I would assume the higher levels of HoL will generally be cleared by guilds or static groups, making it harder for people who aren't in these groups to be able to progress in HoL. After this group clears, there's no reason for them to continue doing HoL for that week. As such, PUBs will have a hard time finding people to run HoL with.
If we add a reward after claiming, then people who have claimed the reward will have a reason to help out other members of the server progress their levels in HoL as well.
The reward shouldn't be big. The goal isn't to make it so that continuing doing the instance is lucrative but rather just give a small reward to incentivize people to help out. I also wouldn't want the reward to be so big that people just continue to run it constantly with their static groups. Additionally, if the cooldown is removed https://forum.muhro.eu/d/3444-hol-waiting-time this can easily become abusable.
As far as what the reward could be, I have seen people mention the temporal gemstone requirement for HoL gears in other threads, so maybe like 1-3 temporal gemstones? or something not HoL related like the diamonds or something idk