Having signed up to destinyclanwars.com now and enjoying the friendly competitive nature against other signed up clans, I feel that maybe this is something missing from the game directly. For a while the point of being in a clan didn't seem so significant thing to do, there isn't much point other than a social gathering and making friends.
There could be several events ongoing each reset, with points scored based on certain stats for each activity. Clans can be segregated into different leagues based on number of members. Awards handed out to Players that achieved certain feats and to clans as a whole who hit ranks 1 to whatever.
This would tie I'm nicely with my other idea on clan shared vaults where materials and glimmer could be shared out amongst its members via the app, and administered by the clan's leaders/Admin.
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This game is anti social supports.