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.