The most common and most likely answer to this crossword clue is the 8 letter word GALACTIC
I've seen this crossword clue in The Guardian
G
A
L
A
C
T
I
C
More clues leading to the result GALACTIC
- Starry celebration given by commander-in-chief? About time
- Extremely big girl, very cold having left boozer finally
- Heavenly festival chief’s entertaining tango
- Stellar celebration by top officer about end of conflict
- Stick around, taking in start of play involving stars
- Festival city mainly erected to house third category of stars
- Very large girl's show is cancelled initially
- Full of stars, Rhode Island’s avoided by festival critic
- Girl in charge of gripping performance of many stars
Buddy explains!

The straight part
We know that "E/x/tremely big" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case e/x/tremely big = galactic.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 GALACTIC mean?
GALACTIC adjective- Of or pertaining to milk, or the secretion of milk.
- Relating to a galaxy.
- Enormous (in size or impact).