Theatre's search for swimmer (9)

I believe the answer is:

globefish

'swimmer' is the definition.
(globefish is a kind of aquatic vertebrate)

'theatre's search' is the wordplay.
'theatre' becomes 'globe' (I've seen this before).
'search' becomes 'fish' (fishing is a kind of searching).
'globe'+'fish'='GLOBEFISH'

'for' acts as a link.

I've seen this clue in The Independent.

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.