"large discretion" is correct and usable in written English.
You can use it when you want to describe a situation in which a person or group of people has the power to make decisions without being held to any specific regulations. For example, "The boss was given large discretion in how to allocate the company's budget."
In its ruling, the Supreme Court declared that federal district courts have "large discretion to model their judgments to fit the exigencies of a particular case".
It also relegates certain remedies to the class of equitable remedies, of which the court has a large discretion to grant or withhold.
Threatened for long periods with Mongol invasion from the northwest and hampered by indifferent communications, the Delhi sultans perforce left a large discretion to their local governors and officials.
This enables the United States to exercise large discretion, by its determination as to whether or not to intervene, as to what cases are reviewable directly in this Court.
The MCCA affords the States large discretion regarding two related variables: the level of the MMMNA, §1396r5(d)(3), and the amount of assets the couple is permitted to retain, §1396r5(f)(2)(A).
Beyond this, however, the state may interfere whereover the public interests demand it, and in this particular a large discretion is necessarily vested in the legislature to determine, not only what the interests of the public require, but what measures are necessary for the protection of such interests.
Great discretion, great loyalty.
The otherworldly side of Holst's music is suggested by the spare and delicate scoring, which uses the large orchestra with discretion.
Mr. Levy explained that the rules for promotion gave teachers and administrators a large amount of discretion in determining whether students would be promoted.
"Beyond the minimum statutory requirements," Ms. Sebelius said, federal officials will give states a large degree of discretion in devising their programs.
These reforms impose stronger economic and bureaucratic discipline on subnational authorities for environmental outcomes, yet preserve large degrees of discretion for achieving central targets.
