static const APlaneClass* planeClassObject;
or
static APlaneClass* planeClassObject;
in the header is just the declaration you are missing
const APlaneClass* APlaneClass::planeClassObject = something;
or
APlaneClass* APlaneClass::planeClassObject = something;
in your PlaneClass.cpp file
but as Phil said the whole thing sounds a little bit wonky.
Would suggest adding a pointer
UPEROPERTY()
APlaneClass* planeClassObject;
into a Manager that could be in a component on the game mode or game state
the UPROPERTY() is important to prevent garbage collection