hold out little hope of something …

Từ điển Oxford Advanced Learner 8th

hold out little, etc. ˈhope (of sth/that…) | not hold out any, much, etc. ˈhope (of sth/that…) idiom
to offer little, etc. reason for believing that sth will happen
•The doctors did not hold out much hope for her recovery.
Main entry: ↑hope_idiom