Bird regularly in bliss (4)
I believe the answer is:
ibis
'bird' is the definition.
(ibis is a kind of bird)
'regularly in bliss' is the wordplay.
'regularly' indicates alternate letters (regularly take one letter, leave next etc.).
'in'+'bliss'='inbliss'
The alternate letters of 'inbliss' are 'IBIS'.
(Other definitions for ibis that I've seen before include "Wader worshipped by ancient Egyptians" , "may be sacred?" , "Wading bird of tropical waters" , "Bird sacred in Ancient Egypt" , "Large wading birds with down-curved bills" .)