The most common and most likely answer to this crossword clue is the 9 plus 4 letter word DANDELION WINE
I've seen this crossword clue in The Times
D
A
N
D
E
L
I
O
N
W
I
N
E
Buddy explains!
The straight part
We know that "home brew" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case home brew = dandelion wine.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.