The most common and most likely answer to this crossword clue is the 11 letter word INHERITANCE
I've seen this crossword clue in The Times
I
N
H
E
R
I
T
A
N
C
E
Buddy explains!

The straight part
We know that "behest" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case behest = inheritance.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 INHERITANCE mean?
INHERITANCE noun- The passing of title to an estate upon death.
- That which a person is entitled to inherit, by law or testament.
- The act or mechanism of inheriting; the state of having inherited
- (genetic algorithms) The biological attributes passed hereditarily from ancestors to their offspring.
- The mechanism whereby parts of a superclass are available to instances of its subclass.