The most common and most likely answer to this crossword clue is the 7 plus 8 letter word FOREIGN MINISTER
I've seen this crossword clue in The Times
F
O
R
E
I
G
N
M
I
N
I
S
T
E
R
More clues leading to the result FOREIGN MINISTER
- One MP’s interfering, so I’m off
- Straw was damaged in strong fire – I’m storing last of rye
- Politician‘s period in power little welcomed by nurse
- Rule scaled down in support for politician
- Be encouraging about time in office, short for politician
- I’m so interfering, travelling as a politician?
- Clergyman from another country, one high up in government
Buddy explains!

The straight part
We know that "One MP" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case one mp = foreign minister.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.