A follow up story is something new that has happened to an already existing news story.
Take Julian Assange for example. He was accused of rape in Sweden, claimed asylum in the Ecuadorean embassy, was evicted, arrested and yesterday jailed for breaching bail conditions.
Each event is a follow on story from what originally happened, Assange being accused of rape.
As this story has gone on for years and years and shows no signs of slowing down, (Assange will appeal against his sentence, and fight extradition to US,) it's the sort of thing your teachers want you to avoid.
Read your local paper, find something fairly straightforward, choose that.