This is the 15985th most frequent Russian word.
проявить
"To show, manifest, or demonstrate."
In this context, 'проявить' means to demonstrate or exhibit an ability or quality, in this case, initiative.
Он может проявить инициативу в этом проекте.
He can show initiative in this project.
Here, 'проявить' refers to the process of developing photographic film or images, used in a technical sense.
Фотографии смогут проявить в лаборатории уже завтра.
The photographs can be developed in the laboratory already tomorrow.
In this sentence, 'проявить' is used in the sense of exercising or showing a trait or attitude, specifically patience.