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

The straight part
We know that "great minds" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case great minds = geniuses.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 GENIUSES mean?
GENIUSES noun- Someone possessing extraordinary intelligence or skill; especially somebody who has demonstrated this by a creative or original work in science, music, art etc.
- Extraordinary mental capacity.
- Inspiration, a mental leap, an extraordinary creative process.
- The tutelary deity or spirit of a place or person.