Martin Davenport had a sister in politics… Beth. But in 2010 she committed suicide on the night of her birthday. When Martin found out later that year that in fact she’d been murdered by an old cab driver, he was devastated. His secondary job still gives him grief to this very day. Every year he goes to her graveside and speaks to her, telling her the stories of the Detective that brought her justice.
The nasal clippers were Sherlock’s horrible attempt to find Martin a birthday/christmas present. Martin felt that having a semi-useless luxury item in his luggage made him seem more like a proper Captain.
Martin is Sherlock and Mycroft’s half brother, conceived during one of their father’s affairs. Martin doesn’t know that the man he calls his father had nothing to do with his conception, but raised him anyway. Sherlock and Mycroft keep their distance from Martin even after his “father’s” death, out of respect for that bond.