Word for when someone gets into a job/role due to being related to someone

Solution 1:

If someone gets a job by being related to someone, it's nepotism

Favoritism granted to relatives or friends regardless of merit.The word nepotism is from the Latin word nepos, nepotis (m. "nephew"), from which modern Romanian nepot and Italian nipote, "nephew" or "grandchild" are also descended.

Peaches Geldof seems to be quite a successful journalist/columnist, television presenter/model celebrity. Probably businesswoman too. I don't know, but I doubt she has no talent at anything she's famous/rich for, and I doubt her father gives or gets her jobs. She's an example of a privileged person. Specifically, as @Tom Au notes, one who is (well-)connected.

Solution 2:

Nepotism is the word you're looking for, although it actually describes any situation where an undue advantage is given to a personal friend or relative in a situation where people should be judged on merit alone.