The most common and most likely answer to this crossword clue is the 7 letter word BIGGEST
I've seen this crossword clue in The Daily Telegraph
B
I
G
G
E
S
T
Buddy explains!
The straight part
We know that "Extremely great" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case extremely great = biggest.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 BIGGEST mean?
BIGGEST adjective- Of great size, large.
- (of an industry or other field, often capitalized) Thought to have undue influence.
- Popular.
- Adult.
- Fat.
- Important or significant.
- (with on) Enthusiastic (about).
- Mature, conscientious, principled; generous.
- Well-endowed, possessing large breasts in the case of a woman or a large penis in the case of a man.
- (sometimes figurative) Large with young; pregnant; swelling; ready to give birth or produce.
- Used as an intensifier, especially of negative-valence nouns
- (of a city) populous
- (of somebody's age) old, mature. Used to imply that somebody is too old for something, or acting immaturely.