the second half of the season
I don`t think there is a one word solution

'Fabiola: You say "In the area of sports, a season is mostly divided into two halves", however this is not necessarily true. While the Bundesliga, for instance, has a winter break and is therefore split into two distinct halves, league football in the UK has no such break and is therefore not perceived as having two halves - indeed it doesn't! The entire concept of Rueckrunde and Hinrunde is thus meaningless in a UK sports context and there are therefore no 1:1 translations.

For your sentence about the German Bundesliga, you have to use myklausunna's solution:

"January sees the start of the second half of the Bundesliga season"

"The second half of the Bundesliga season begins in January"