Hibernian goddess with aspiration (5)
I believe the answer is:
irish
'hibernian' is the definition.
(I've seen this before)
'goddess with aspiration' is the wordplay.
'goddess' becomes 'iris' (Greek goddess of the rainbow).
'with' says to put letters next to each other.
'aspiration' becomes 'h' (speech sound from a puff of breath).
'iris'+'h'='IRISH'
(Other definitions for irish that I've seen before include "Eg, native to Dublin" , "Hibernian -- breed of 4" , "of European country" , "Of this place" , "W European" .)