Cannot Get a new Radiant Quest from Companions in Skyrim

Im Not 100% This Will Help But...

According To The Wiki You Need

  • Must have at least one Glenmoril Witch Head in inventory.

  • Must complete at least 1 Radiant Quest from Farkas or Vilkas, after completing Glory of the Dead and having Glenmoril Witch Heads in inventory.

If That Doesn't Help The Wiki (Link Below) Will Have A Bug List It Will Help Find Out What You Need To Do To Fix It

Source: http://elderscrolls.wikia.com/wiki/Purity_%28Quest%29

EDIT: It May Be This Bug

There appears to be a bug when you accept Vilkas's Purity quest before Farkas. The quest status will switch to the Completed even though you haven't completed it. Also Vilkas will not follow you to Ysgramor's Tomb. To resolve this, accept and finish Farkas's Purity quest first and be sure that the quest giver is following you the whole way through.

Source: Same As Above