Cartomancy is an intuitive reading with modern gaming cards instead of the Tarot deck. Some people think our modern cards came from the minor arcana of the Tarot, others say they started at the same time. Either way, both decks started as a game, and then evolved into a tool for insight and intuition. Since the suites are similar, I am in the camp that reads playing cards as being very similar to a minor arcana-only Tarot reading.
I read the king of clubs much as I would the King of Wands in a Tarot reading, with two particular aspects to the clubs/wands/batons card. The obvious facet is leadership. The King is leader, for good or for ill. Clubs and wands tend to draw my attention to things like spiritual development, personal growth, character, integrity, philosophy…that sort of thing. The card can hint at leadership skills, or in taking personal responsibility for your beliefs, words and action. The latter of those two seems to be the more common in readings I’ve done. If you want another aspect, there is always the more Jungian approach…the card may be asking you to consider you own inner assertive, “Yang” side…where it might either be too strong or lacking, particularly with respect to the ideas of personal responsibility and leadership.