What does the cryptic crossword clue "Complex play on Rome lost in the battle (11)" mean?

The definition is "battle". The wordplay uses an anagram. anagram of PLAY + ROME + THE = THERMOPYLAE; definition: "battle" The answer is THERMOPYLAE.

Complex play on Rome lost in the battle (11)

Independent Cryptic #11023 | 18 Across | 2022-02-10 flower