Sadly its a known issue and about 2 years old
it's something the web team need to fix but is currently a low priority. Fingers crossed it will be fixed soon.
I've also copied the response Mod Lyon gave which Sicariu has quoted on his Clan Help thread.
Why won’t my clan’s motif/banner/vexillum update on our Clan Page?
There is currently a caching issue on Jagex’s end that prevents Clan Banners from updating on Clan Pages. Based on our observations, this issue began around December 2017 and has yet to be fixed.
The issue has been addressed on the forums by Mod Lyon (23 May 2018):
Original message details are unavailable.
Hey there,
Frankly we're super busy with ... literally everything.. right now, hence why we haven't replied sooner.
The problem is a caching issue on our side not refreshing the banner, unfortunately there's not a solution I can give you that I'm aware of. Further, this isn't something that's going to be fixed for some time.
If there are any more updates or I'm corrected by another JMod I'll let you know. Until then I'm afraid its something you're going to have to grin and bear.
Apologies,
Mod Lyon
Another reply from Mod Lyon (22 July 2019):
Mod Lyon
said
:
Unfortunately, while some of the issues you've mentioned are no brainers such as fixing the clan flags, it's not something that's considered to be a priority at this time.
Hopefully we'll get some time to work on these in the future, but at the moment we're dealing with much more pressing issues which require our attention.
This post will be updated if/when more information regarding the issue is made available.