“Speed regime” is also a specialized term. As I understand it, “speed regime” refers roughly to the combination of things needed to achieve a certain type of speed.
As I understand your sentence, it means the pilot has to control various different aspects of flight all at the same time, and has to ensure that these different aspects work together in such a way that the plane remains level.
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The sentence can be rewritten as: “To hold the airplane in level flight, the pilot must adjust angle of attack and thrust appropriate for the flying speed.” Does that help?
For an airplane to be in level flight, the airplane thrust has to be equal to airplane drag and the lift to be equal to the airplane weight. You adjust the angle of attack to change lift. You adjust thrust to overcome the drag.