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 knickers on
To stay calm; to not get flustered or angry.
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.
keep one's nose clean
To stay out of trouble, especially by avoiding unlawful behavior.