The most common and most likely answer to this crossword clue is the 11 letter word SUBCONTRACT
I've seen this crossword clue in The Times
S
U
B
C
O
N
T
R
A
C
T
Buddy explains!

The straight part
We know that "Let out" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case let out = subcontract.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 SUBCONTRACT mean?
SUBCONTRACT noun- A portion of a contracted project that is contracted out in turn.
- To contract out portions of a larger contracted project.