Listening to internal murmurs, one American religious group shifted almost completely to Iona (12)

'listening to internal murmurs' is the definition.
(listening to the sounds of internal organs)

'one american religious group shifted almost completely to iona' is the wordplay.
'one' becomes 'a'.
'american' becomes 'us' (abbreviation for United States).
'religious group' becomes 'cult' (I've seen this before).
'shifted' is an anagram indicator.
'almost completely' means to remove the last letter.
'to' with its last letter removed is 't'.
't'+'iona'='tiona'
'tiona' with letters rearranged gives 'ation'.
'a'+'us'+'cult'+'ation'='AUSCULTATION'