The most common and most likely answer to this crossword clue is the 10 letter word ALPHABETIC
I've seen this crossword clue in The Guardian
A
L
P
H
A
B
E
T
I
C
More clues leading to the result ALPHABETIC
Buddy explains!

The straight part
We know that "like characters in set" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case like characters in set = alphabetic.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 ALPHABETIC mean?
ALPHABETIC adjective- Of or relating to an alphabet, especially the characters A to Z, both uppercase and lowercase.