One swearing in audition shows on-screen presence (6)
I believe the answer is:
cursor
'on-screen presence' is the definition.
(present on a computer screen)
'one swearing in audition' is the wordplay.
'one swearing' becomes 'curser'.
'in audition' shows a homophone (sound like) (audition can mean hearing).
'curser' is a homophone of 'CURSOR'.
'shows' is the link.
(Other definitions for cursor that I've seen before include "Feature of computer" , "Indicator on computer monitor" , "Computer arrow" , "Indicator on a visual display" , "Computer screen marker" .)