The most common and most likely answer to this crossword clue is the 10 letter word SUCCESSION
I've seen this crossword clue in The Guardian
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More clues leading to the result SUCCESSION
Buddy explains!

The straight part
We know that "Following" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case following = succession.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 SUCCESSION mean?
SUCCESSION noun- An act of following in sequence.
- A sequence of things in order.
- A passing of royal powers.
- A group of rocks or strata that succeed one another in chronological order.
- A race or series of descendants.
- Rotation, as of crops.
- A right to take possession.
- In Roman and Scots law, the taking of property by one person in place of another.
- The person who succeeds to rank or office; a successor or heir.