Thirteen
It's not just (or all) about emotions in this comparison. Quick note here: it is a typical misunderstanding that the other suits lack emotions--Swords are anxieties/harmony, Wands passion/temper and Pents grounded/shame; Cups are the emotions that make you smile or tear-up, the mushy emotions which, at their highest, lead to joy, and at their lowest depression. So, your King/Swords isn't unemotional--when he sees a beautiful balance, as in science or art, he gets that wonderful feeling we all have, now and then, of discovering the larger universe outside ourselves.So more possibly like Pastor at a church? Or some organization/community where it was ran and or govered with love and empathy than by say a group that felt they would have to repress their emotions bc of said structure.
Back to King/Cups & Hierophant: Cups aren't just emotions. They are also spirituality. Like the emotions, they're the "softer" sprituality of, say, heartfelt prayer. This as compared to the passionate spirituality (preacher type) of Wands, or the practial spirituality of rituals (Pents) or the theological debates of Swords. Which is to say, yes, as the Knight/Cups can sometimes be on a spiritual quest as much as a quest for love (love of the divine), so the King/Cups can be one who has found such love. As a King, he would see it as his destiny to share it and use it to guide his family/people. This connects him to the Hierohant who feels a similar motivation. Both can be spiritual leaders in that father figure/teacher/guide mode.
And both, it should be noted, can (in the negative) feel they know what's best for others and not be willing to let others find their own way via their own path/mistakes.