The most common and most likely answer to this crossword clue is the 11 letter word MINISTERIAL
I've seen this crossword clue in The Times
M
I
N
I
S
T
E
R
I
A
L
More clues leading to the result MINISTERIAL
- Short series of episodes about television's top executive
- Like priests in Times unusually backing animal shelter…
- Concerned with the cloth of skirt tailor retails
- Government department’s small and it’s real crazy!
- Short series of episodes involving leader in thrall of a government department
- Executive on the government side
- Governmental taxman at first seen in short TV drama
Buddy explains!

The straight part
We know that "executive" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case executive = ministerial.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 MINISTERIAL mean?
MINISTERIAL noun- A member of the mediaeval estate or caste of unfree nobles.
- Related to a religious minister or ministry.
- Related to a governmental minister or ministry.
- Having the power to wield delegated executive authority.
- Serving as an instrument or means (i.e., procedural or ancillary, not substantive).