My new beau, naked, is a bit of a looker (6)
I believe the answer is:
cornea
'a bit of a looker' is the definition.
(I've seen this before)
'my new beau naked' is the wordplay.
'my' becomes 'cor' (both are expressions of surprise).
'new' becomes 'n' (common abbreviation eg NT for New Testament).
'naked' says to take the centre (outside letters removed so centre is unclothed).
The central letters of 'beau' are 'ea'.
'cor'+'n'+'ea'='CORNEA'
'is' is the link.
(Other definitions for cornea that I've seen before include "Transparent part of the coat of the eyeball" , "Outer covering of the eye" , "Front covering of eye" , "It covers the eye" , "Observer section?" .)