The most common and most likely answer to this crossword clue is the 9 letter word DEPONENTS
I've seen this crossword clue in The Times
D
E
P
O
N
E
N
T
S
More clues leading to the result DEPONENTS
Buddy explains!

The straight part
We know that "they’ll testify" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case they’ll testify = deponents.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 DEPONENTS mean?
DEPONENTS noun- A witness; especially one who gives information under oath, in a deposition concerning facts known to him or her.
- (grammar) A deponent verb.