To stay calm; to not get flustered or angry.
keep one's pants on
To stay calm.
keep one's hair on
To stay calm; to be patient; to calm down.
keep a cool head
To keep one's cool; to stay calm.
keep one's temper
To remain calm; to avoid becoming angry or annoyed.
keep up with the times
To change one's ideas, views or way of living in order to stay current…
hold one's nerve
To stay calm facing nervousness.