The Oxford Dictionary defines horsepower as a unit of power equal to 550 foot-pounds per second. Because horsepower represents the total produced power of a system, however, it is not directly relatable to thrust.
Thrust is calculated by subtracting absorbed power from produced power; therefore, is calculated on a per-situation basis. For example, to determine the thrust produced by a car, you must know not only the air resistance created by the car's body but also the dynamic friction of its tires on the ground and even the energy lost by the vehicle's drive-train.
Because horsepower is defined as force-over-distance over time, the best way to envision it is as the energy put into a system. Because thrust is defined as the energy exerted by a system in motion, the best way to picture it is as the output of a system. Together, you cannot calculate the produced thrust without knowing the system that is transmitting the energy.