The most common and most likely answer to this crossword clue is the 7 plus 8 letter word CABINET MINISTER
I've seen this crossword clue in The Daily Telegraph
C
A
B
I
N
E
T
M
I
N
I
S
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R
More clues leading to the result CABINET MINISTER
- Press church to restrain island's senior politician
- Best incriminate revolutionary member of the government
- One carrying red box around, in case one’s needed in church
- Chaotic — a bit reminiscent of Grayling, perhaps
- This Conservative in Britain meets in desperation?
- Nice man is bitter after reshuffle, no longer being one?
- Wild time in bars etc in May perhaps
- Irregular bet incriminates leading politician
- Scandalous bet incriminates member of government
- Console member of the clergy and senior politician
Buddy explains!

The straight part
We know that "member of government" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case member of government = cabinet 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.