as soon as it arrives; upon arrival
Used for items, documents, or things that arrive; also for a person's arrival. Follows a noun or verb stem.
We will contact you as soon as the product arrives.
He started the meeting as soon as he arrived.
到着次第 is a fixed compound meaning 'as soon as it arrives'; 次第 alone is a suffix meaning 'as soon as' or 'depending on'.
Compound of 到着 (arrival) + 次第 (as soon as).