Authors often start by giving the characters strong initial personalities. For example, if a character is from a proud and noble house, they might be initially haughty in the face of an arranged marriage. Then, through interactions with their betrothed, they start to change. Maybe they learn humility or compassion.
Another way is through the character's goals. If a character's main goal is to gain power, an arranged marriage to someone with influence could be a strategic move. But as they get to know their spouse, they might realize that there are other things in life worth more than power. So, the character develops from being power - hungry to someone who values love and loyalty, all within the context of the arranged marriage story.