Automatic succession to first-born child (13)

I believe the answer is:

primogeniture

(Other definitions for primogeniture that I've seen before include "(Right of) being first-born" , "Eldest-takes-all system" , "Right of inheritance belonging exclusively to the eldest son" , "Firstborn-inherits system" , "State of being the firstborn" .)

I've seen this clue in The Guardian.

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