The most common and most likely answer to this crossword clue is the 7 letter word COHABIT
I've seen this crossword clue in The Guardian
C
O
H
A
B
I
T
More clues leading to the result COHABIT
- . Slightly supportive of Charlie and other half initially going to live together
- Before it nothing’s gained by playing Bach live together
- Conservative and old Independent bath prepared to shack up together
- Company practice to share accommodation
- Live together in cold house, upset slightly
- Business custom is to share accommodation
- Manx cat and I both, weirdly, live together
- Company custom to maintain an intimate in-house relationship
- Officer and husband briefly live together
- Lives with company procedures
Buddy explains!

The straight part
We know that "shack up together" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case shack up together = cohabit.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 COHABIT mean?
COHABIT verb- To live together with someone else, especially in a romantic and sexual relationship but without being married.
- To coexist in common environs with.
- To engage in sexual intercourse; see coition.