Star has gone down? Not quite (3)
I believe the answer is:
sun
'star' is the definition.
(the Sun is a star)
'gone down? not quite' is the wordplay.
'gone down?' becomes 'sunk' (I've seen this in another clue).
'not quite' means to remove the last letter (most but not all of the word).
'sunk' with its final letter taken off is 'SUN'.
'has' acts as a link.
(Other definitions for sun that I've seen before include "Hub of our planetary system" , "It's sol in Latin" , "Centre of a solar system" , "Major star" , "Warmer" .)