As soon as the mail carrier arrives, he hurries out to collect the mail.
Literal
Postal-delivery-person [subject-が] come-[conditional-と] immediately, he [topic-は] hurry-[then-で] mail [object-を] receive-[to-に] go.
~とすぐに ('as soon as X, immediately after X') stacks the automatic-result conditional ~と with the adverbial すぐに ('immediately') — an emphatic 'right away' pattern. 受け取り is the noun form of 受け取る ('to receive, take'), and に marks the purpose of 行く ('go to receive'). A tidy subordinating chain.