The most common and most likely answer to this crossword clue is the 8 letter word RESERVED
I've seen this crossword clue in The Times
R
E
S
E
R
V
E
D
More clues leading to the result RESERVED
Buddy explains!

The straight part
We know that "Booked/saying little" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case booked/saying little = reserved.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 RESERVED mean?
RESERVED verb- To keep back; to retain.
- To keep in store for future or special use.
- To book in advance; to make a reservation.
- To make an exception of; to except.
- Slow to reveal emotion or opinions.
- Set aside for a particular person or purpose.