The most common and most likely answer to this crossword clue is the 4 plus 5 plus 4 letter word LORD PRIVY SEAL
I've seen this crossword clue in Financial Times
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More clues leading to the result LORD PRIVY SEAL
- Solver rapidly worked out “senior cabinet minister”
- Peer over lavatory, close, to see senior minister
- Off-duty senior cabinet member seen in toilet in cricket ground, having drunk ale
- Minister left perched on the end of my toilet seat
- Corrupt old earl’s hanging round outside toilet for minister
- God can confirm minister
- Lovers rapidly besmirched cabinet minister
- Senior cabinet minister provides rally in reshuffle
Buddy explains!

The straight part
We know that "Off-duty senior cabinet member" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case off-duty senior cabinet member = lord privy seal.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.