The most common and most likely answer to this crossword clue is the 3 letter word REX
I've seen this crossword clue in Independent
R
E
X
More clues leading to the result REX
Buddy explains!

The straight part
We know that "king" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case king = rex.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 REX mean?
REX noun- An animal which has a genetic recessive variation that causes the guard hairs to be very short or fully lacking.