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.