The most common and most likely answer to this crossword clue is the 3 letter word SIS
I've seen this crossword clue in Independent
S
I
S
More clues leading to the result SIS
Buddy explains!

The straight part
We know that "Family member" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case family member = sis.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does SIS mean?
SIS noun- A daughter of the same parents as another person; a female sibling.
- A female member of a religious order; especially one devoted to more active service; (informally) a nun.
- Any butterfly in the genus Adelpha, so named for the resemblance of the dark-colored wings to the black habit traditionally worn by nuns.
- A senior or supervisory nurse, often in a hospital.
- Any woman or girl with whom a bond is felt through common membership of a race, profession, religion or organization, such as feminism.
- (sometimes capitalized) A black woman.
- A form of address to a woman.
- A woman, in certain labour or socialist circles; also as a form of address.
- An entity that has a special or affectionate, non-hierarchical relationship with another.
- A node in a data structure that shares its parent with another node.
- (usually attributively) Something in the same class.