First to get rubbish to cave (6)
I believe the answer is:
grotto
'cave' is the definition.
(grotto is a kind of cave)
'first to get rubbish to' is the wordplay.
'first to' says to take the initial letters.
'rubbish' becomes 'rot' (both can mean nonsense).
The first letter of 'get' is 'g'.
'g'+'rot'+'to'='GROTTO'
(Other definitions for grotto that I've seen before include "It's left on Dec 24 by Santa and his reindeer" , "Attractive natural, or artificial, cave" , "Pretty cave" , "Fancy cave" , "A picturesque cave as in Lourdes (6)" .)