Cryptic crossword clue
Mischief-maker’s in the Home Counties, meeting English monarch in pursuit of own interests 4-7

The most common and most likely answer to this crossword clue is the 4 plus 7 letter word SELF SEEKING

I've seen this crossword clue in Financial Times
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Buddy explains!

The straight part
We know that "in pursuit of own interests" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case in pursuit of own interests = self seeking.
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 SELF SEEKING mean?

SELF SEEKING noun
  1. The selfish promotion of one's own interests.
SELF SEEKING adjective
  1. Mindful of, or promoting, only one's own interests.
  2. (of a missile) That searches for a target automatically.

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