Out with almost all the rubbish (5)
I believe the answer is:
offal
'the rubbish' is the definition.
(I've seen this in another clue)
'out with almost all' is the wordplay.
'out' becomes 'off' (I've seen this before).
'with' is a charade indicator (letters next to each other).
'almost' means to remove the last letter (almost the whole word is kept).
'all' with its final letter taken off is 'al'.
'off'+'al'='OFFAL'
(Other definitions for offal that I've seen before include "Edible internal parts" , "Meaty waste" , "Less edible parts of animal, entrails and organs" , "Liver, kidney, etc, as food" , "Liver, lungs etc" .)