The most common and most likely answer to this crossword clue is the 6 letter word EVELYN
I've seen this crossword clue in Financial Times
E
V
E
L
Y
N
More clues leading to the result EVELYN
- Regularly putting note to the last name
- Still keeping extremely lovely 17th- century recorder
- Man or woman going up many levels but not all
- Waugh visiting Kiev, Ely, Naples
- Two women, one who kept diary
- Two ladies and another, who could be a man
- Just holding covers for literary chronicler
- The Spanish, consumed by misplaced envy for the diarist
- Man or woman regularly name dropping
- Knievel evacuating Yukon, calling for war?
Buddy explains!

The straight part
We know that "one who kept diary" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case one who kept diary = evelyn.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.