The phrase "exercise great discretion" is correct and usable in written English.
It can be used when advising someone to be careful and judicious in their decision-making or actions.
Example: "In sensitive situations, it is important to exercise great discretion to avoid misunderstandings."
Alternatives: "use careful judgment" or "apply sound judgment."
One may well argue that this is a necessary, and even a good thing -- that America's contemporary internationalist superpower status requires a muscular and nimble president able to exercise great discretion abroad, but still subject to congressional checks.
Exercise great discretion when handling these as the administrator of the memorial – if it's venting from a family member, you may wish to contact them privately.
I agree that requiring reporters to exercise greater discretion in when and how they choose to attribute information to "anonymous sources" would result in readers' benefiting from more diligent and responsible reporting.
The whip rules that will operate at the Cheltenham Festival next week will come into force on Tuesday following the publication by the British Horseracing Authority on Monday of detailed guidelines to allow stewards to exercise greater discretion when deciding if a rider has breached the regulations.
The debate about welfare is cast as an effort to allow the states to exercise greater discretion over conditions of eligibility.
And while the department's budget was set by the legislature, she exercised great discretion over compensation.
His battered armed forces will have a hard time doing so and, indeed, Iraqi jets have exercised great discretion in their encounters with their infinitely more sophisticated American adversaries.
At the same time we must remark, that however powerful and useful they may be as an instrument, they cannot be used with safety without considerable knowledge of the peculiar subjects, and without the exercise of great discretion in drawing results.
In view of his prestige as a literary man, accepted by large sections of public opinion in matters not related to writing, it is the recommendation of the Legal Attaché at Havana that great discretion be exercised in avoiding an incident with Ernest Hemingway".
Great discretion, great loyalty.
"We have great discretion," McKnight said.
