Divine being in Halifax regularly with daughter (5)
I believe the answer is:
naiad
'divine being' is the definition.
(naiads are spirits in Greek myth)
'in halifax regularly with daughter' is the wordplay.
'regularly' indicates alternate letters (regularly take one letter, leave next etc.).
'with' means one lot of letters go next to another.
'daughter' becomes 'd' (genealogical abbreviation).
'in'+'halifax'='inhalifax'
The alternating letters of 'inhalifax' are 'naia'.
'naia'+'d'='NAIAD'
(Other definitions for naiad that I've seen before include "Greek mythological water nymph" , "spirit in water" , "divine female figure" , "Mythological water-nymph" , "River nymph" .)