Mute panic when swimming is related to air supply (9)
I believe the answer is:
pneumatic
'related to air supply' is the definition.
(pneumatic can mean using air or gas)
'mute panic when swimming' is the wordplay.
'when swimming' indicates an anagram.
'mute'+'panic'='mutepanic'
'mutepanic' with letters rearranged gives 'PNEUMATIC'.
'is' acts as a link.
(Other definitions for pneumatic that I've seen before include "Driven by compressed air" , "Concerned with air, gases or wind" , "form of drill?" , "Using compressed air" , "Type of drill" .)