The most common and most likely answer to this crossword clue is the 10 letter word IMPEACHING
I've seen this crossword clue in Financial Times
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More clues leading to the result IMPEACHING
Buddy explains!

The straight part
We know that "what some think Trump needs" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case what some think trump needs = impeaching.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 IMPEACHING mean?
IMPEACHING verb- To hinder, impede, or prevent.
- To bring a legal proceeding against a public official.
- To charge with impropriety; to discredit; to call into question.
- To demonstrate in court that a testimony under oath contradicts another testimony from the same person, usually one taken during deposition.