The most common and most likely answer to this crossword clue is the 8 letter word OVERTURE
I've seen this crossword clue in The Daily Telegraph
O
V
E
R
T
U
R
E
More clues leading to the result OVERTURE
- Finished by Tuesday? That’s about right for this work
- Start, having passed river on time
- Against entering rocky route on approach
- Reverse cut by English opener?
- Proposal to provide public with running water
- Proposal concerning trade union engineers
- Obvious regret, dropping resistance to second proposal
- Approach open river
- Open University engineers getting advance
- Open vessel to capsize
Buddy explains!

The straight part
We know that "The Hebrides maybe" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case the hebrides maybe = overture.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 OVERTURE mean?
OVERTURE noun- An opening; a recess or chamber.
- Disclosure; discovery; revelation.
- (often in plural) An approach or proposal made to initiate communication, establish a relationship etc.
- A motion placed before a legislative body, such as the General Assembly of the Church of Scotland.
- A musical introduction to a piece of music.
- To make overtures; to approach with a proposal.