The phrase "a major exception is" is correct and usable in written English.
You can use it when introducing a significant deviation from a general rule or statement.
Example: "Most animals are cold-blooded, but a major exception is the leatherback sea turtle, which can regulate its body temperature."
Alternatives: "a significant exception is" or "a notable exception is".
A major exception is Stanford, which has raised more in recent years than any other American university.
(A major exception is "Seize the Day," which is formally perfectly realized. But that book is a novella, a day in the life. It doesn't require a plot).
While it appears that many lead creative positions have been entrusted to foreign filmmakers, a major exception is the director himself.
But a major exception is in the offing with the Bush-era tax cuts, which are set to lapse on Jan 1.
A major exception is the lone building that survived the atomic bombing of Hiroshima whose steel dome top has become a globally recognized symbol of the reality of nuclear warfare.
A major exception is the writer Miguel Ángel Asturias (1899 1974), a poet and novelist who won the Lenin Peace Prize in 1966 and the Nobel Prize for Literature in 1967.
A major exception was the week or two each year that he and his parents spent at retreats and conferences for the highly gifted.
A major exception was a lusty blues rendition of "One for My Baby (and One More for the Road)," in which she flirted with gut-busting volume, building the song up slowly to a crest, before gradually subsiding.
Rebecca Tarbotton was a female 30-something in a universe of environmental leaders dominated by male 50-somethings (a major exception being her mentor, Michael Brune, 41, now the executive director of the Sierra Club).
He wrote little fiction after becoming a teacher, a major exception being "On Venus, Have We Got a Rabbi," published in 1974 in a Jewish-themed anthology called "Wandering Stars," which tackles the question of whether a Hebrew-speaking alien that looks like a "wrinkled and twisted" brown pillow with short gray tentacles can be considered a Jew.
A major exception was Price's purchase of Innate Immunotherapeutics shares for between $50,001 and $100,000.
