Hereditary earl comes up in draw started by government (7)

I believe the answer is:

genetic

I'm a little stuck... Click here to teach me more about this clue!

'hereditary' is the definition.
(I know that hereditary can be written as genetic)

I don't understand the remainder of the clue.

Can you help me to learn more?

(Other definitions for genetic that I've seen before include "Pertaining to heredity" , "(The code) of our DNA" , "relating to origin" , "Relating to heredity" , "coming from a common source" .)

I've seen this clue in The Independent.

Want a hint initially instead of a full solution? Install my app