The most common and most likely answer to this crossword clue is the 6 letter word NEARBY
I've seen this crossword clue in The Times
N
E
A
R
B
Y
More clues leading to the result NEARBY
- Close bank up in the city
- Tight times just round the corner
- Close Scottish bank set up in US financial centre
- English dons raced back to get Times locally
- Drink coming up with Spooner in the vicinity
- Similar times? That’s handy
- Close finishes in Open absorb many, holding attention
- Handy underwear, longing to hold it up
- Close attention applied to book set in New York
- Appreciation shown by bishop in US state neighbouring
Buddy explains!

The straight part
We know that "locally" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case locally = nearby.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 NEARBY mean?
NEARBY adjective- Adjacent, near, close by
- Next to, close to