The most common and most likely answer to this crossword clue is the 6 letter word PARKER
I've seen this crossword clue in The Guardian
P
A
R
K
E
R
More clues leading to the result PARKER
Buddy explains!
The straight part
We know that "2 great/2 great/2 great/2 great/2 great/2 great/2 great/2 great/2 great" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case 2 great/2 great/2 great/2 great/2 great/2 great/2 great/2 great/2 great = parker.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.