The phrase "a quick study with" is correct and usable in written English.
It can be used to describe someone who learns or understands new information or skills rapidly, often in a specific context or subject area.
Example: "She is a quick study with new software, mastering it in just a few hours."
Alternatives: "fast learner in" or "quick to grasp".
Mr. Chenault described Mr. Akerson as a quick study with strong strategic skills and a "fierce competitive drive".
She proved a quick study with the hula hoop game (gyrating in circles), before finding her long-sought treadmill replicated in the running game.
I'm usually a quick study with sports, and I've been drawn in recent years to activities that require a half-decent sense of balance.
Mr. Giesser -- as usual, his own director -- is obviously a quick study with a sense of humor, but surely not all the laughs he gets with this story were intended.
Time for some good news then: Dr. Smith is a bold and charismatic stylist, and here he was working with the guitarist Peter Bernstein, an experienced partner, and the drummer Bill Stewart, a quick study with open ears (and a lot of history with Mr. Bernstein).
How many high school kids would do that?" Her United States team coach, Terry Steiner, called Montgomery a quick study with a great appetite for learning and added: "She is always calm and that could be her downfall in the Olympics.
Suppose someone wants to make a quick study of a topic with which he or she is not familiar say, evolution.
It was like falling off a log because Mary is such a quick study, and her facility with language is pretty breathtaking.
Denise Craigen, Air Force wife, sees her cross-country moves as an advantage, saying travel "makes her easy to work with and a quick study".
Arroyo was a quick study who could change hands with his whip deftly and keep a horse racing on the bit.
Bainbridge's elliptical account of the realities of Britain as a growing imperialist power fixes together gritty war reportage with a quick study of the emergent technology of photography.
