Bit of rubbish in hut (the tiniest bit) (5)
I believe the answer is:
shred
'the tiniest bit' is the definition.
(I've seen this in another clue)
'bit of rubbish in hut' is the wordplay.
'bit of' says to take the initial letters.
'in' indicates putting letters inside.
'hut' becomes 'shed' (I've seen this in another clue).
The first letter of 'rubbish' is 'r'.
'r' put inside 'shed' is 'SHRED'.
(Other definitions for shred that I've seen before include "Cut into tiny pieces" , "Tatter; small amount" , "Cut into small pieces" , "Scrap of material" , "Cut into bits" .)