The most common and most likely answer to this crossword clue is the 4 plus 9 letter word HOME SECRETARY
I've seen this crossword clue in Financial Times
H
O
M
E
S
E
C
R
E
T
A
R
Y
More clues leading to the result HOME SECRETARY
- In private, I agree to receive Republican minister
- Government Minister? Sadly they care more about status, primarily
- May’s three core wobbles, as a minister
- Theresa May disheartened and pissed with core minister
- This writer has confidence in white-haired minister
- Some treachery undoes cabinet minister
- Minister in PA
- British cabinet minister, old as the hills, keeping me hidden
Buddy explains!

The straight part
We know that "minister" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case minister = home secretary.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.