The most common and most likely answer to this crossword clue is the 7 letter word SPHERES
I've seen this crossword clue in The Daily Telegraph
S
P
H
E
R
E
S
More clues leading to the result SPHERES
- Leader in Strictly now appearing in extremely prestigious balls
- Special present: square balls
- Fields of activity of all round significance
- Fields of activity he gets a mixed press about
- Wasp he researched gathers in fields
- Areas where head of state is apprehensive, reportedly
- Special reducing dissension for circles of society
- Leaders of society paying service around here? Indeed!
- They look round, quietly present on board
- Free press hangs about man's circles
Buddy explains!

The straight part
We know that "fields" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case fields = spheres.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 SPHERES mean?
SPHERES noun- A regular three-dimensional object in which every cross-section is a circle; the figure described by the revolution of a circle about its diameter .
- A spherical physical object; a globe or ball.
- The apparent outer limit of space; the edge of the heavens, imagined as a hollow globe within which celestial bodies appear to be embedded.
- Any of the concentric hollow transparent globes formerly believed to rotate around the Earth, and which carried the heavenly bodies; there were originally believed to be eight, and later nine and ten; friction between them was thought to cause a harmonious sound (the music of the spheres).
- An area of activity for a planet; or by extension, an area of influence for a god, hero etc.
- The region in which something or someone is active; one's province, domain.
- The set of all points in three-dimensional Euclidean space (or n-dimensional space, in topology) that are a fixed distance from a fixed point .
- The extension of a general conception, or the totality of the individuals or species to which it may be applied.
- To place in a sphere, or among the spheres; to ensphere.
- To make round or spherical; to perfect.