The most common and most likely answer to this crossword clue is the 6 letter word DOMAIN
I've seen this crossword clue in The Times
D
O
M
A
I
N
More clues leading to the result DOMAIN
Buddy explains!

The straight part
We know that "kingdom" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case kingdom = domain.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 DOMAIN mean?
DOMAIN noun- A geographic area owned or controlled by a single person or organization.
- A field or sphere of activity, influence or expertise.
- A group of related items, topics, or subjects.
- The set of all possible mathematical entities (points) where a given function is defined.
- The set of input (argument) values for which a function is defined.
- A ring with no zero divisors; that is, in which no product of nonzero elements is zero.
- An open and connected set in some topology. For example, the interval (0,1) as a subset of the real numbers.
- Any DNS domain name, particularly one which has been delegated and has become representative of the delegated domain name and its subdomains.
- A collection of DNS or DNS-like domain names consisting of a delegated domain name and all its subdomains.
- A collection of information having to do with a domain, the computers named in the domain, and the network on which the computers named in the domain reside.
- The collection of computers identified by a domain's domain names.
- A small region of a magnetic material with a consistent magnetization direction.
- Such a region used as a data storage element in a bubble memory.
- (data processing) A form of technical metadata that represent the type of a data item, its characteristics, name, and usage.
- The highest rank in the classification of organisms, above kingdom; in the three-domain system, one of the taxa Bacteria, Archaea, or Eukaryota.
- A folded section of a protein molecule that has a discrete function; the equivalent section of a chromosome