It is not possible to apply for the 1st semester in the summer semester. Applications for the 1st semester can only be submitted for the winter semester.

However, applications for higher semesters in the summer semester are possible. For the requirements, see https://www.stat.de/archives/ufaqs/can-i-apply-for-higher-study-semesters-hohere-fachsemester .

Otherwise, you could register as guest student (“Nebenhörer”) to already take some courses in the summer semester and then apply for the winter term, for HU see the corresponding information of the course guidance centre on the HU website.