According to the cover note of the manga volume 5, new anime of Kämpfer was announced to be aired next March. Judging from the note, it is probably a special episode(s), not a new season.

A "new project" of Kämpfer was announced last September. A PV of the project will be shown at Comiket 79 to be held from Dec 29th - 31st.

According to the official website, the title of the new anime is " Kämpfer für die Liebe".

Sources: Scan of the cover note, Kämpfer anime official twitter, Kämpfer official website

Updated on December 31st
According to Starchild Mania, Kämpfer für die Liebe is a two-episode special. They are designated as Episode 13 and 14, and the first episode is a direct sequel to the previous series and the second episode is about the trans-sex of Naturu.

Source: Scan of StarCha Mania

Updated on March 7th
According to MyCom Journal, only episode 14 will be aired on TV. The episode 13 will be released in the Blu-ray & the DVD on May 25th.

Source: MyCom Journal