The most common and most likely answer to this crossword clue is the 10 letter word CISTERCIAN
I've seen this crossword clue in Independent
C
I
S
T
E
R
C
I
A
N
More clues leading to the result CISTERCIAN
- Monk having nun— one imprisoned?
- Man following order spies held inside tank
- Order tank to carry spies
- Order for stone coffin someone from the West Midlands once executed
- 3 Monk withdrawing just so rite can change
- One obeying order to surround agents with tank
- Man following order put spies inside tank
- Well, going round about Iowa with a member of a white brotherhood...
- Brother I see sent up after relative losing head in prison
- One holding a flush, clubs and one ace being put in order
Buddy explains!

The straight part
We know that "Man following order" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case man following order = cistercian.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.