Firstly, let’s look at the word “indulgence.”
Indulgence means to give in to or satisfy a desire or wish.
I’ll indulge myself today have a cookie.
It means that I will satisfy my desire by having a cookie.
To ask for someone’s indulgence means that you are asking them to give you permission to do or take part in something that you want to do or have. Many times, the term “ask for your indulgence” is used when asking for a person’s attention or participation in a formal setting.
May I ask for your indulgence to please join me in the living room for a game of cards?”
To crave someone’s indulgence means that you have a strong desire for their approval or permission for you to do something that you want to do. It’s often used when people are very dependent on another person. For example in a child – parent relationship.
Tommy always craves his father’s indulgence. He wants his father’s approval for everything he does