"master the ability" is correct and usable in written English.
You can use it to talk about learning a particular skill or becoming proficient in a specific area. For example, "He worked hard to master the ability to speak Spanish fluently."
Instead, he suggested, schools should offer classes in arithmetic numeracy, insuring that students master the ability to read a corporate report or to parse the federal budget.
You master the ability to lose yourself in the game, because that's what you need to do to not be conscious of being conscious.
It takes time and practice to master the ability to shift your state of mind and create sustainable change in your emotions, words, and deeds.
You master the ability to lose yourself in the game, because that's what you need to do — to not be conscious of being conscious.
Those who seek out people and situations foreign to them and master the ability to assimilate are far more likely to be successful in a world that's becoming both bigger and smaller at the same time.
Master the ability to move production among plants by using interchangeable and generic parts in many products, relying on similar and even identical plant designs and processes across the company, and cross-training employees.
"They have mastered the ability to produce significant amounts of fissile material.
Success now requires not just doing it better, but mastering the ability to do it differently.
The North has conducted a nuclear test, but it is unclear whether the country has mastered the ability to deliver a working nuclear weapon.
Neural networks have mastered the ability to label things in images, and now they're learning to tell stories from a set of photos.
Though using a medium and a technology that were still in their infancy, Kertész mastered the ability to capture spontaneous activity without sacrificing thoughtful composition.
