Butterfly has a holiday, having captured the heart of Pinkerton, a naval officer (5,7)
I believe the answer is:
'butterfly' is the definition.
(white admiral is a kind of butterfly)
'a holiday having captured the heart of pinkerton a naval officer' is the wordplay.
'a holiday' becomes 'whit' (whitsun).
'having captured the heart of' indicates the central letters.
'a naval officer' becomes 'admiral' (I've seen this before).
The central letter of 'pinkerton' is 'e'.
'has' is the link.
(Other definitions for white admiral that I've seen before include "Describing doctor's oath", "Butterfly - with a Daimler (anag)".)