Hand to: Daenerys Targaryen
Under Joffrey, Tyrion was constantly trying to keep his head above water serving a horrible king among selfish people who only valued influence and favors. Not exactly the place for someone who prizes real knowledge and accomplishments like Tyrion to really thrive. Under Daenerys, however, he's a well-needed voice of reason and wisdom for a fierce leader, who truly values what he brings to the table. Sure, his record hasn't been perfect (ahem, that "deal" with the slave masters?), but Daenerys knows a good adviser when she sees one. No wonder he swore to serve as her counsel forever.
When it comes to a good balance between ruler and Hand, this one might be perfect: an experienced Hand with knowledge of Westerosi politics who truly believes in his queen and an ambitious, badass ruler who has no problem showing her power but still recognizes that she can learn a lot from those around her.
