The most common and most likely answer to this crossword clue is the 8 letter word DEPOSING
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More clues leading to the result DEPOSING
Buddy explains!

The straight part
We know that "giving testimony" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case giving testimony = deposing.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 DEPOSING mean?
DEPOSING verb- To put down; to lay down; to deposit; to lay aside; to put away.
- To remove (a leader) from (high) office, without killing the incumbent.
- To give evidence or testimony, especially in response to interrogation during a deposition
- To interrogate and elicit testimony from during a deposition; typically done by a lawyer.
- To take or swear an oath.
- To testify; to bear witness; to claim; to assert; to affirm.