The most common and most likely answer to this crossword clue is the 6 letter word HAYMOW
H
A
Y
M
O
W
Buddy explains!

The straight part
We know that "stack up in a barn" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case stack up in a barn = haymow.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 HAYMOW mean?
HAYMOW noun- A pile of hay stored in a barn.
- The place in a barn where hay is deposited.