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exposure to the chance of injury or loss; a hazard or dangerous chance:
It’s not worth the risk.
Insurance.

the hazard or chance of loss.
the degree of probability of such loss.
the amount that the insurance company may lose.
a person or thing with reference to the hazard involved in insuring him, her, or it.
the type of loss, as life, fire, marine disaster, or earthquake, against which an insurance policy is drawn.

to expose to the chance of injury or loss; hazard:
to risk one’s life.
to venture upon; take or run the chance of:
to risk a fall in climbing; to risk a war.
at risk,

in a dangerous situation or status; in jeopardy:
families at risk in the area of the weakened dam.
under financial or legal obligation; held responsible:
Are individual investors at risk for the debt part of the real estate venture?

take / run a risk, to expose oneself to the chance of injury or loss; put oneself in danger; hazard; venture.
noun
the possibility of incurring misfortune or loss; hazard
(insurance)

chance of a loss or other event on which a claim may be filed
the type of such an event, such as fire or theft
the amount of the claim should such an event occur
a person or thing considered with respect to the characteristics that may cause an insured event to occur

at risk

vulnerable; likely to be lost or damaged
(social welfare) vulnerable to personal damage, to the extent that a welfare agency might take protective responsibility

(Austral, informal) no risk, an expression of assent
take a risk, run a risk, to proceed in an action without regard to the possibility of danger involved in it
verb (transitive)
to expose to danger or loss; hazard
to act in spite of the possibility of (injury or loss): to risk a fall in climbing
n.

1660s, risque, from French risque (16c.), from Italian risco, riscio (modern rischio), from riscare “run into danger,” of uncertain origin. The anglicized spelling first recorded 1728. Spanish riesgo and German Risiko are Italian loan-words. With run (v.) from 1660s. Risk aversion is recorded from 1942; risk factor from 1906; risk management from 1963; risk taker from 1892.
v.

1680s, from risk (n.), or from French risquer, from Italian riscare, rischaire, from the noun. Related: Risked; risks; risking.

risk (rĭsk)
n.

The possibility of suffering a harmful event.

A factor or course involving uncertain danger, as with smoking or exposure to radiation.

In danger, as in Their house’s location on the San Andreas Fault puts them at risk in the next major earthquake. [ c. 1900 ]
Legally responsible to pay for loss or damage, as in If he can’t keep up with the insurance premiums, he is at risk for any liability claims on the property. [ Late 1700s ]
In addition to the idiom beginning with
risk
also see:

at risk
calculated risk
run a risk