I'm going to compete in an upcoming intercollegiate tennis tournament.
I'm going to play in a tennis tournament between different universities at the end of this month.
ーI'm going to compete in an upcoming intercollegiate tennis tournament.
「今度のインカレのテニストーナメントに出場します」
to compete で「競う・参加する」
intercollegiate で「大学間の・大学対抗の」
ーI'm going to play in a tennis tournament between different universities at the end of this month.
「今月末、大学間のテニストーナメントでプレーします」
to play in a tennis tournament between different universities のようにも表現できます。
ご参考まで!