The most common and most likely answer to this crossword clue is the 7 letter word NUCLEUS
I've seen this crossword clue in The Sunday Telegraph
N
U
C
L
E
U
S
More clues leading to the result NUCLEUS
- Setter flips about changed clue for atomic base
- Heart of uncle, possibly Uncle Sam
- Star’s upset over cryptic clue’s focus
- Relative backing UN ahead of US central component
- The heart of the matter is that uncle is out to get us
- Core muscle, with miles gone, stretched by character in Marathon
- Core family member having upset top couple and me, royally
- Benefactor promoting new American centre
- Uncle out to get us — that’s the heart of the matter
- Core group of students to welcome around the French university
Buddy explains!

The straight part
We know that "Core" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case core = nucleus.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 NUCLEUS mean?
NUCLEUS noun- The core, central part of something, around which other elements are assembled.
- An initial part or version that will receive additions.
- The massive, positively charged central part of an atom, made up of protons and neutrons.
- A large membrane-enclosed organelle found in eukaryotic cells which contains genetic material.
- A ganglion, cluster of many neuronal bodies where synapsing occurs.
- The central part of a syllable, most commonly a vowel.