Fetching details from the dictionary...

earnest; sincere; acute; keen; fervent
pressing; urgent; serious; severe
pertinent; appropriate
彼女の切実な訴えに心を動かされずにはいられない。
I can't help but be moved by her earnest appeal.
少子高齢化は切実な社会問題として認識されている。
The declining birthrate and aging population are recognized as pressing social issues.
切実な問題を見て見ぬ振りはできない。
I can't turn a blind eye to such an urgent problem.