One of the last quest of the chain requires you to gather The Splintered Throne requires you to acquire 50 Shadowfrost Shards. We didn't know the droprates until recently, the official armory has been updated with most of the data from patch 3.3 and gave us a few numbers :

• Shards only drop in 25-man from any boss of the instance.
• 25-man normal mode bosses have a medium (25-50%) chance to drop a shard.
• 25-man heroic mode bosses have a high (51-99%) chance to drop a shard.

If we assume that you kill all the boss in hard modes you should get an average of 9 shards each week and it will take 6 weeks to upgrade Shadow's Edge to Shadowmourne
You now have all the info you need to decide who gets it in your guild. Make sure you check the Shadowmourne Preview if you missed it!