AC not cooling using heat pump
If the outdoor fan comes on and the compressor does not, you need a "hard start kit"
this is either a potential relay and start capacitor as in my diagram or a PTC thermistor solid state start assist device that piggy backs onto the run capacitor.
This is assuming your compressor is cold to the touch and has not been starting.
If your compressor has been starting and is off due to the thermal overload being open
Then it is due to  the capacitor being bad or refrigerant being low or the compressor is mechanically tight or electrically shorted to itself internally, this is not something a homeowner will usually be able to do unless walked through it step by step.