1
general::
Delay until the end of something, as in They waited out the war in Paris. This expression comes from baseball, where it alludes to the batter refraining from swinging at pitches in the hope of being walked (getting to first base on balls). It was first recorded in 1909 and was transferred to other activities by the 1930s.
American Heritage Idioms
2
general::
Phrase(s): wait something out
to wait until something ends. • I will wait the summer out, and if nothing happens, I’ll write again. • I can wait out the storm inside.
McGrawhill's American Idioms And Phrasal Verbs