The most common and most likely answer to this crossword clue is the 6 letter word BRANCH
I've seen this crossword clue in Financial Times
B
R
A
N
C
H
More clues leading to the result BRANCH
- Bishop organised church's regional office
- Bishop managed church – part of a big organisation
- British and American farm department
- Bishop organised church’s regional office
- Bishop managed church division within large organisation
- Section of British farm
- Part of tree bough’s first spread
- British farm just one part of the business
- … bough with top of bough spread
- Opening of big estate for shoot
Buddy explains!

The straight part
We know that "department" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case department = branch.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 BRANCH mean?
BRANCH noun- The woody part of a tree arising from the trunk and usually dividing.
- Any of the parts of something that divides like the branch of a tree.
- A creek or stream which flows into a larger river. (compare Ohio, Pennsylvania and West Virginia run, and New York and New England brook.)
- One of the portions of a curve that extends outwards to an indefinitely great distance.
- A location of an organization with several locations.
- A line of family descent, in distinction from some other line or lines from the same stock; any descendant in such a line.
- A local congregation of the LDS Church that is not large enough to form a ward; see Wikipedia article on ward in LDS church.
- An area in business or of knowledge, research.
- A certificate given by Trinity House to a pilot qualified to take navigational control of a ship in British waters.
- A sequence of code that is conditionally executed.
- A group of related files in a source control system, including for example source code, build scripts, and media such as images.
- A branch line.
- To arise from the trunk or a larger branch of a tree.
- To produce branches.
- To (cause to) divide into separate parts or subdivisions.
- To jump to a different location in a program, especially as the result of a conditional statement.
- To discipline (a union member) at a branch meeting.