There's a few bits of rules to sift through here. These quotes are from the D&D Compendium.
Direct the Strike provokes opportunity attacks
Ranged and Area Powers Provoke: If an enemy adjacent to you uses a ranged power or an area power, you can make an opportunity attack against that enemy.
Direct the Strike is a ranged power - you're targeting any individual within a range of 5. Under normal circumstances, it would provoke an opportunity attack.
Staff Expertise feat
In addition, when you make a ranged or an area attack with a staff as an implement, you don’t provoke opportunity attacks for doing so.
So as long as you can cast Direct the Strike "with a staff as an implement", you don't provoke an OA. However, Direct the Strike doesn't have the Implement keyword, so this might not apply. It doesn't have the Weapon keyword either, so implement-as-a-weapon rules don't apply. So does it count as casting it with the implement?
This needs interpretation
The rules here are unclear. Staff Expertise was published in books from 2010 - Heroes of the Fallen Lands and Heroes of the Forgotten Kingdoms. To understand what they were trying to say, we're going to have to do some historical comparison.
Later books, like Mordenkainen's Magnificent Emporium, used a different and more specific wording. For instance, Forceful weapons have this description:
Whenever you pull, push, or slide a target with an implement attack using a forceful implement, you can increase the distance of the forced movement by 1 square.
By contrast, in Staff Expertise's case, it reads like using any ranged power. In addition, it says "with an implement" not "using an implement", so one could interpret this as just incidentally having the implement in hand whilst not using it. However, HotFK and HotFL also include a feat named Axe Expertise:
You gain a +1 feat bonus to weapon attack rolls you make with an axe.
This clues us in on their language. By "with", they mean "using". Someone who's an expert with an axe shouldn't be getting attack bonuses to sword attacks because they're holding an axe in their other hand.
So by recent standards it should read more like this:
In addition, when you make a ranged or an area attack using a staff as an implement, you don’t provoke opportunity attacks for doing so.
No, you can't use Staff Expertise with Direct the Strike. Direct the Strike provokes an OA even if you have Staff Expertise.
You cannot use an implement to cast a non-implement power, and you cannot use Direct the Strike via your staff. Staff Expertise only applies when you can do that, and so it doesn't apply.