The most common and most likely answer to this crossword clue is the 8 letter word FIREDAMP
I've seen this crossword clue in The Times
F
I
R
E
D
A
M
P
More clues leading to the result FIREDAMP
- Got rid of a sitting member, a horror of mine
- Sacked a politician for inflammatory release
- Hazard in mine dismissed by a politician
- Gas let off by a politician
- Got rid of a politician, that’s a hazard of mine
- Problem of mine stimulated a politician
- Mining hazard got rid of a politician
- Shot a politician revealing explosive stuff
Buddy explains!

The straight part
We know that "a horror of mine" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case a horror of mine = firedamp.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 FIREDAMP mean?
FIREDAMP noun- An inflammable gas (mostly methane) found in coal mines; forms an explosive mixture with air.