The most common and most likely answer to this crossword clue is the 9 letter word REPUTABLE
I've seen this crossword clue in The Sunday Telegraph
R
E
P
U
T
A
B
L
E
More clues leading to the result REPUTABLE
- Trustworthy theatre board accommodating Feydeau's last
- Upright piano used in reel composed with tuba
- Trustworthy salesman sitting on university board
- Regarded as fair, like a shot it’s OK to take again just one time?
- Respected salesman with superior furniture
- Well-respected place besieged by a rebel, unfortunately
- Cooked pure supply of food that’s kosher
- Pure nonsense, board trustworthy
- Queen’s revolving set fitted upright
- . Honourable member associated with university board
Buddy explains!

The straight part
We know that "trustworthy" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case trustworthy = reputable.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 REPUTABLE mean?
REPUTABLE adjective- Having a good reputation; honourable.