A hickey is a bruise in the skin. TO CONCEAL WITH MAKEUP: green neutralizes red, so if the hickey is redish in color, dab a green concealer directly over it first. Then use your regular skin-color foundation or concealer and powder on top. If you don't neutralize the redish blotch with green, the hickey will usually triumph.
Be sure to dab the concealer on rather than rubbing it in. If you don't have green, use an oil-based concealer that is lighter than your natural skin color, as the hickey color will cause it to look darker. But focus the application of the lighter concealer only on the hickey area. Otherwise, the area will look like a big smudge and everyone will know. Scarves and high-necked colars can help, unless you're a guy.