this season; the current season
Refers to the present or current season in a broad sense, including sports seasons, TV/anime seasons, fashion seasons, and seasonal business periods. It can be used as a noun or adverbially to mean 'this season.'
It is my favorite drama of this season.
The team has not lost even once this season.
He announced that he will retire at the end of this season.
They earned their first win of the season.
This campaign is only for this season.
A new coach took over starting this season.
来季 means 'next season,' the direct opposite of 今季 'this season.'
今期 and 今季 are both read こんき, but 今期 refers to a defined term such as a fiscal or school period, while 今季 specifically refers to a season.
A Sino-Japanese compound of 今, meaning 'now' or 'current,' and 季, meaning 'season.' The spelling directly reflects the meaning 'current season.'