The most common and most likely answer to this crossword clue is the 4 letter word GRAN
I've seen this crossword clue in The Daily Telegraph
G
R
A
N
More clues leading to the result GRAN
- Old lady managed to follow golf
- She had pop award reduced
- Member of family, 23, participated in marathon maybe
- Older relative – nearly 1,000?
- Experienced woman taking £800?
- Foremost of girl’s relatives always nurturing
- Pop rang his mum
- Relation called, last character to come forward
- Relative in rocking chair, drama queen, all conclude
- Elderly relative‘s fragrant
Buddy explains!

The straight part
We know that "senior family member" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case senior family member = gran.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 GRAN mean?
GRAN noun- (usually affectionate) a grandmother
- A grandfather