A news from Hibike! Euphonium official website has mentioned the second season TV Series will start on October. Unfortunately, no further information were added. We just need to be patient. Sooner or later, I am sure Kyoto Animation will tease us with more information. Earlier today, there is a roadshow of Hibike! Euphonium. The four main casts and Sakurai Takahiro were present. I am sure the second season was announced there.
— 劇場版 響け！ユーフォニアム (@anime_eupho) April 23, 2016
Hibike! Euphonium is an anime about music, specifically orchestra. The second season should pick the story where the first season left. The ending of the first season is already very satisfying, so my expectation with the second season is really really high. Especially this anime is coming from Kyoto-Animation.