The most common and most likely answer to this crossword clue is the 5 plus 2 letter word STAYS ON
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More clues leading to the result STAYS ON
Buddy explains!

The straight part
We know that "Royal heir (Prince Charles) pissed off that Brenda (Queen Elizabeth II) does so" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case royal heir (prince charles) pissed off that brenda (queen elizabeth ii) does so = stays on.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.