I claim the ornamental design for a hanger clip installation tool, as shown and described.
FIG. 1 is a perspective view of an embodiment of the hanger clip installation tool according to the design, with the elements in phantom forming no part of the claimed design;
FIG. 2 is a right side planar view of the design, with the elements in phantom forming no part of the claimed design;
FIG. 3 is a front planar view of the design, with the elements in phantom forming no part of the claimed design;
FIG. 4 is a rear planar view of the design, with the elements in phantom forming no part of the claimed design;
FIG. 5 is a left side planar view of the design, with the elements in phantom forming no part of the claimed design;
FIG. 6 is a top planar view of the design, with the elements in phantom forming no part of the claimed design; and,
FIG. 7 is a bottom planar view of the design, with the elements in phantom forming no part of the claimed design.