The most common and most likely answer to this crossword clue is the 7 plus 6 letter word CARRIES WEIGHT
I've seen this crossword clue in The Times
C
A
R
R
I
E
S
W
E
I
G
H
T
Buddy explains!
The straight part
We know that "is significant" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case is significant = carries weight.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.