One coming out over master getting promoted? That's rubbish (6)
I believe the answer is:
debris
'rubbish' is the definition.
(debris is a kind of rubbish)
'one coming out over master getting promoted?' is the wordplay.
'one coming out' becomes 'deb' (I've seen this in another clue).
'over' says to put letters next to each other (in a down clue, some letters go over others).
'master' becomes 'sir' (a schoolmaster may be addressed as sir).
'getting promoted?' says the letters should be written backwards (in a down clue, letters go up).
'sir' back-to-front is 'ris'.
'deb'+'ris'='DEBRIS'
'that's' is the link.
(Other definitions for debris that I've seen before include "Refuse, litter" , "Rubble as of fallen building" , "Rubble, detritus" , "Rebids for rubble" , "Rubble, lots of broken pieces" .)