to look anxiously for; to wait eagerly for
Example sentences
彼は彼女のたよりを待ち望んでいる。
He is anxious for her news.
生徒だけでなく先生も休暇を待ち望んでいる。
Not only the student but their teacher is looking forward to holiday.
私は君との再会を待ち望んでいる。
I am looking forward to seeing you again.