Investigators report that there have been some 'hopeful' developments in the case.
a presidential 'hopeful' [=a person who hopes to become president]
There are 'hopeful' signs that the crisis may end soon.
(..) Jon Snow... They all fell in love with you. Jon Snow is not in love with me. Oh, my mistake. I suppose he stares at you longingly because he's hopeful for a successful military alliance. He's too little for me. I didn’t mean... As heroes go he is quite little. I know you're brave. (..)2017 TvShow: Game of Thrones Title: Beyond the Wall Season: 7 Episode 6