World Trigger, Gate: Jieitai Kanochi nite, Kaku Tatakaeri Recommendations
Both of those anime are about a Gate which suddenly appeared in Japan, and monsters came out of it.
In both of them the monsters are pushed back and even the people go to the other world to fight and investigate
A gate to another world opens in Japan and the government has to do something about it.
Young men are trained to fight the unknown enemies coming from the other side.
Both also share military routine as a theme, though Border Organization in World Trigger is a bit different from usual military headquarters.
New Dimension appearing and monster coming out to destroy or conquer everything.
Similar aspect where both animes is connected to another world.