The most common and most likely answer to this crossword clue is the 9 letter word BACKTRACK
I've seen this crossword clue in The Times
B
A
C
K
T
R
A
C
K
More clues leading to the result BACKTRACK
Buddy explains!

The straight part
We know that "Reverse one’s opinion" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case reverse one’s opinion = backtrack.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 BACKTRACK mean?
BACKTRACK noun- The act of backtracking
- To retrace one's steps.
- To repeat or review work already done.
- To taxi down an active runway in the opposite direction to that being used for takeoff.
- To exercise a racehorse around the racetrack in the opposite direction to that in which races are run.