Doing extremely well in a job or at school, and clearly heading for the top. It sits in front of a noun — a high-flying executive, a high-flying student, a high-flying career — and it does two things at once: it says the person is very successful, and it says they are moving upward fast. That upward movement is the heart of it, so it fits a young lawyer being promoted every year better than an old, settled, comfortable one. It is common in newspapers and in workplace talk, and it is admiring, though sometimes with a small breath of 'and we shall see how long that lasts', because English likes to follow flying with falling. The word is also used in its plain, literal sense — high-flying birds, a high-flying plane — and the meaning is decided by what follows it. Beside it stands the noun 'high-flier' (or 'high-flyer'), the person themselves; the two are used together freely.