1
general::
Also, run the risk. Be subjected to danger, as in Hiding anything from customs means running a risk that you'll be caught, or Without the right postage and address, this package runs the risk of being lost. [Mid-1600s]
American Heritage Idioms
2
general::
Phrase(s): run a risk (of something) [and] run the risk (of something)
to take a chance that something (bad) will happen. • I don’t want to run the risk of losing my job. • Don’t worry. You won’t have to run a risk.
McGrawhill's American Idioms And Phrasal Verbs