During the last update to ELITE, Beachhead accidentally let information on Clan Challenges leak (its now removed). As you see in the image above, there are going to be Daily Clan Challenges, and Weekly Clan Challenges. Clan Challenges will be for both Premium and Free members, but nothing specific has been announced at this time.
Beachhead Studio has acknowledged the fact that Clan Challenges are in development, but they are focusing on Clan Operations. With this leak it seems they are very close to being done.