1
general::
Seek to become a participant in, as in I'm going out for soccer. [First half of 1900s] Also see GO FOR, def. 3; GO IN FOR, def. 2.
American Heritage Idioms
2
general::
Phrase(s): go out for someone or something
to leave in order to bring back someone or something. • Albert just went out for a newspaper. • Fran went out for Bob, who was on the back porch, smoking a cigarette.
McGrawhill's American Idioms And Phrasal Verbs