I want to know how the drama will develop/progress

While "ドラマ" refers to a TV drama in Japan, typically "a drama" in English refers to a theatrical play (on stage etc.), unless you say "a TV drama."
So I'll take it as you are talking about a theatrical play in this case. In that context, when you say "how the drama will develop or progress," it would mean how the play on stage will proceed, in a way that no one (actors nor the audience) would know how the play on stage would unfold because they are improvising it etc.
If you are talking about a TV drama, you could probably say "I want to know how the story (of the show, or the TV drama) will develop/progress."