The most common and most likely answer to this crossword clue is the 10 letter word HEMISPHERE
I've seen this crossword clue in The Times
H
E
M
I
S
P
H
E
R
E
More clues leading to the result HEMISPHERE
- Border is quiet at these points, one either side of equator
- Global section of border company providing connections present
- Ambassador with PM is for transforming present section of world
- Half the world is into cannabis at this point
- Man with ship at sea in simple part of world
- Edge is said to be dread part of the world
- Border company with connections present global 50-per-cent share?
- Half of the world’s leading historians make the ambassador break up the crumbling empires
- Earth has two alien empires heh?
Buddy explains!

The straight part
We know that "one either side of equator" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case one either side of equator = hemisphere.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 HEMISPHERE mean?
HEMISPHERE noun- Half of the celestial sphere, as divided by either the ecliptic or the celestial equator .
- A realm or domain of activity .
- Half of the Earth, such as the Northern Hemisphere, Southern Hemisphere, Western Hemisphere or Eastern Hemisphere, Land Hemisphere, Water Hemisphere etc. .
- Any half-sphere, formed by a plane intersecting the center of a sphere. .
- A map or projection of a celestial or terrestrial hemisphere .
- Either of the two halves of the cerebrum. .