1
general::
Also, in hopes that;in the hope of or that;in high hopes of or that. Expecting and wishing for, as in We went in hopes of finding a vacancy, or They met in the hope of bringing about a peaceful settlement. The phrases with that are used with clauses, as in In hopes that something good might come of it, he began to work, or We are in high hopes that a cure for leukemia will be found soon. [c. 1600]
American Heritage Idioms
2
general::
Phrase(s): in (high) hopes of something
Fig. expecting something. • I was in hopes of getting there early. • We are in high hopes that John and Mary will have a girl.
McGrawhill's American Idioms And Phrasal Verbs