Clock Zero ~Shuuen no Ichibyou~

Kurou Nadeshiko is the twelve year old daughter of some wealthy high class members. She goes to a wealthy school with her childhood friend and hopes to become a doctor one day. However, every night she has a dream about being in another world. That world is full of ruins and she is ten years older. One day, a transfer student named Kaido Takato comes to her class and she gets involved in an after school extra-curricular club which they call “Clock Zero”.

(Edited from Hinano's Game Babbles)