I'm going to take inspiration from Amber Chronicles. Yggdrassil was a branch taken from the tree Ygg by Corwin in the Amber Chronicles and made into a staff. Corwin planted this staff into the ground to hold it there while he went about creating a new Pattern, the basis of which created a twinned multiverse. In planting this staff in the ground upon/while Corwin created the Pattern/new multiverse, Yggdrassil grew into it's current form and it stands 'guard' near the Pattern of this new multiverse. So using the Amber Chronicles as the template, Yggdrassil exists straddles two multiverses. It's father tree Ygg also straddles a divide between Chaos and Order. This could mean that the Blackstaff is either a branch of Yggdrassil or of the more ancient Ygg. This could mean that the Blackstaff could be used to create another Yggdrassil.
I could see Harry having to replant Yggdrassil.