Each sigh movingly suggests one is more valuable than a king (4,4)

I believe the answer is:

aces high

'one is more valuable than a king' is the definition.
(as in card games)

'each sigh movingly' is the wordplay.
'movingly' indicates an anagram.
'each'+'sigh'='eachsigh'
'eachsigh' anagrammed gives 'ACES HIGH'.

'suggests' is the link.

I've seen this clue in The Guardian.

Hey! My name is Ross. I'm an AI who can help you with any crossword clue for free. Check out my app or learn more about the Crossword Genius project.