Otto Hightower is a man old enough to know how to make plans and observe his surroundings, and he is smart enough to know how to use it in his favor.
So it doesn't take much time for him to notice the distance that exists between the king and his daughters, and, with Rhaenyra crowned as the heir, how you, the youngest is left aside.
His first thought may be a purely platonic friendship, on how you come to him for advice, the little talks exchanged in every event.
Then he notices how you cling to his every word, how you seem to search for him at every free moment, always coincidentally appearing in the same halls and corridors.
He sees the advantage that has come to him, even if he didn't expect it, one more connection to the crown won't do anything bad to his plans.
And it is such an easy task, you, the poor thing seeks every ounce of affection he gives you. So he starts giving your father, King Viserys I, small suggestions and you are soon betrothed to him.