Trudi Canavan's
Traitor Spy triology fits, but I'm not sure how well it works if you haven't read
The Black Magician triology first (which is about a novice learning magic).
Mary Robinette Kowal's Glamourist histories, a five-book series, starting with
Shades of Milk and Honey. The protagonist does get better in magic during the series, but she's an accomplished glamourist as the beginning of the first book. In this world, magic is subtle, illusions and not fireballs.