To Sponsor
To Promote
If 主催 is sponsorship, the verb version of that would be to sponsor.
しゅさいする
This is a jukugo word, which usually means on'yomi readings from the kanji. If you know the readings of your kanji you'll know how to read this as well. It will help to know the word 主催 already as well.
うちの学校で土曜日にカラオケパーティーを主催するんだけど、よかったら来ない？
Our school is hosting a karaoke party this Saturday. Would you like to join us?