Both sentences are correct and can mean the same situation, but the mental position is different.
In the first phrase, the speaker is imaging the situation that Eleys has arrived at Nara someday in the future and he is speaking from that point of time. So Eleys "has already come", and he is going to see her by car.
In the second phrase, the speaker's consciousness remains at the present time. In this case, Eleys may come "in the future", then he will pick her up.