If I play Portable Portal at a battlefield and then react with Legends Jarvan to move a unit to that battlefield, can I pay Portable Portal’s power cost to ready the unit that was moved there?

No — Portal's ready can't hit the unit Jarvan moves, because the move hasn't happened yet when you lock in Portal's choice.

Two corrections to the framing first: Jarvan's line isn't something you activate in reaction — it's a triggered ability that fires off playing the Deploy gear. And it triggers at the same moment as Portal's own "when you play this" play effect (both go on the chain once Portal resolves onto the battlefield), so you pick the order but both are put on the chain — costs paid, unit chosen — before either one resolves (CR 355.5.b). By the time Portal's trigger resolves, Jarvan's move is still sitting resolved-after, so the only legal unit choices are ones already at that battlefield.

Worth noting the ready is usually moot anyway: an effect-based move like Jarvan's doesn't exhaust the unit, so it arrives in whatever state it was in — this line only "fails" if you were counting on re-readying a unit that was already exhausted before the move. Portal can still ready any friendly unit that was already there, and Jarvan still moves the unit to that battlefield.