The most common and most likely answer to this crossword clue is the 11 letter word SECRETARIAT
I've seen this crossword clue in The Daily Telegraph
S
E
C
R
E
T
A
R
I
A
T
More clues leading to the result SECRETARIAT
- Office staff restricted air temperature
- Upwardly mobile valuer in City of London having posed outside an office
- Careerist worked a short time in admin department
- Body once dictated to?
- Admin area in Tate’s racier after refurbishment
- People in administration uncommunicative, with air getting tense
- Fancy caterers at one government office
- Underground air turbulence at administrative department
- Create a stir playing “Horse”
- Unseen rodeo rope missing the first horse
Buddy explains!

The straight part
We know that "admin department" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case admin department = secretariat.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 SECRETARIAT mean?
SECRETARIAT noun- The office or department of a government secretary.