I missed my flight, but can I get on the next one?

Literal

Airplane [onto-に] missed [but-が], next-one [onto-に] can-ride [question-か]?

乗り遅れる is a compound verb meaning 'to miss (a vehicle)' — 乗る (ride) + 遅れる (be late). The が softens the transition to the request. 次のに uses の as a pronoun ('the next one') followed by に marking the vehicle.