Sign of life in bather swimming around (6)
I believe the answer is:
breath
'sign of life' is the definition.
(breathing shows someone is alive)
'bather swimming around' is the wordplay.
'swimming around' is an anagram indicator.
'bather' is an anagram of 'BREATH'.
'in' is the link.
(Other definitions for breath that I've seen before include "Bertha (anag.)" , "Air drawn in and expelled out" , "Inhale and exhale air" , "Slight movement of air" , "Air that's inhaled and exhaled" .)