A/your bounden duty
Definition 1 of 1
Pro Tip 1/3Moral Weight
The phrase emphasizes a heavy moral responsibility, suggesting a very important or serious duty. 
As a judge, delivering justice is your bounden duty.
Pro Tip 2/3Old-fashioned Tone
Using 'a/your bounden duty' can sound old-fashioned or formal. It's rarely used in casual conversation. 
You speak of a bounden duty, like a knight of old.
Pro Tip 3/3Literary Use
This phrase is often used in literature, especially in historical or fantasy contexts, to evoke a traditional sense of honor. 
You have a bounden duty to your clan, to uphold its honor.