The most common and most likely answer to this crossword clue is the 7 letter word VICINAL
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The straight part
We know that "local" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case local = vicinal.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.
Crossword Answer definitions
VICINAL adjective- Of or pertaining to a neighborhood; neighboring.
- Describing identical atoms or groups attached to nearby (especially adjacent) atoms in a molecule.
- Describing subordinate planes on a crystal, which are very near to the fundamental planes in angles, and sometimes take their place.