Galadriel's

[Raynor]

I agree with Selmo on her greed for power, however I would insist more on Lorien being the object of her greed.

Originally Posted by Chapter IX, Silmarillion

No oaths she swore, but the words of Feanor concerning Middle-earth had kindled in her heart, for she yearned to see the wide unguarded lands and to rule there a realm at her own will.

I would say she had quite a high standing among the elves already while being in Valinor, due to her innate skills and beauty, and by being a direct descendent of the ruler of all the Noldor in the blessed realms.

However, one thing she lacked there was having a land she could actually rule. Even if you "claim" a parcel there, who in their right mind would say "I am an uncontended ruler of this land" - not when the Valar are right under your nose, and you know them in their majesty fully revealed. On the other hand, Middle-Earth does seem to be outside the direct influence of the valar, and finding, claiming, ruling and defending your own realm there makes more sense and appeases more the thirst for power.