The most common and most likely answer to this crossword clue is the 7 letter word BENCHER
I've seen this crossword clue in The Guardian
B
E
N
C
H
E
R
Buddy explains!
The straight part
We know that "Senior Inn Member" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case senior inn member = bencher.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 BENCHER mean?
BENCHER noun- A senior member of a law society in a Canadian province (except New Brunswick).
- One of the senior governing members of an Inn of Court.
- An alderman of a corporation.
- A member of a court or council.
- One who frequents the benches of a tavern; an idler.