{出|で}る・{出|だ}す = lit. to leave・to make something leave (transitive pair).

suddenly start doing

〜出す

is used to indicate the unexpected or sudden beginning of an action

走り出す To break out into a dash

買い出す To suddenly begin buying things

部屋に入るとすぐに彼女は手紙を読み出した。 On entering her room, she began to read the letter.