I am strongly intersted in buying "The Legend of Heroes: Trails in the Sky", but as it is the first part of a trilogy, I wonder whether the game ends with some sort of closure or rather with a harsh cliffhanger?

Maybe someone who has already played the game can comment on this question.

The main plot of the game gets wrapped up quite nicely, but the game also ends on somewhat of a cliffhanger. Fortunately, the sequel is set to come out this winter which picks up exactly where this game leaves off.

I read somewhere that part one ends with a cliffhanger and part two closes the story. Part three only answers some open questions.

Yeah, part 1 ends with a cliffhanger. Legend of Heroes 6 is composed of three games that are direcly sequels (not sure for third). The end is something like Soul Reaver 1 to 2.