Run after (someone) or (something)
To chase someone.The young boys ran after the small dog.
Run afoul of (someone or something)
To get into trouble with someone or something.The young man ran afoul of the law and got into much trouble.
Run across (someone or something)
To meet someone unexpectedly, to find something unexpectedly.I ran across an old friend in the library.
Run a tight ship
To be very strict and organized when managing an organization or your life.My friend runs a tight ship and makes few mistakes in his life.
Run a risk of (something)
To be open to danger or loss.You run a risk of going to jail if you drive after drinking.
Run a fever/temperature
To have a body temperature higher than normal.The little boy was running a fever so his parents decided to call the doctor.
Rump session
A meeting held after a larger meeting.After the convention, I attended a rump session which was very interesting.
Rule the roost
To be the dominant figure in a family.The woman seems rather quiet but she rules the roost in her family.
Rule out (someone or something) rule (someone or something) out
To decide against or eliminate someone or something.The police ruled out the man as a possible bank robber.
A rule of thumb
A basic or accepted pattern or rule.It is a rule of thumb in the fire department that nobody goes into a burning building by themselves.