What does the cryptic crossword clue "Hats Pete brandished are favourite bugbears (3,5)" mean?

The definition is "bugbears". The wordplay uses an anagram. anagram of HATS + PETE = PETHATES; definition: "bugbears" The answer is PETHATES.

Hats Pete brandished are favourite bugbears (3,5)

Daily Mail Cryptic #17149 | 8 Down | 2023-07-26 flower