Wife visits Iona naked? That's personal! (3)
I believe the answer is:
own
'personal' is the definition.
(eg one's own possessions are personal possessions)
'wife visits iona naked?' is the wordplay.
'wife' becomes 'w' (abbreviation).
'visits' is an insertion indicator (visit can mean to go into).
'naked?' says to take the centre (outside letters removed so centre is unclothed).
The centre of 'iona' is 'on'.
'w' put within 'on' is 'OWN'.
'that's' is the link.
(Other definitions for own that I've seen before include "Be in legal possession of (3)" , "Acknowledge" , "Possess - recognise - admit" , "Allow" , "Control" .)