Tear your old top off, it's dirty (6)
I believe the answer is:
earthy
'it's dirty' is the definition.
(I've seen this before)
'tear your old top' is the wordplay.
'your old' becomes 'thy' ('thy' historically meant 'your').
'top' means to remove the first letter.
'tear'+'thy'='tearthy'
'tearthy' with its first letter taken off is 'EARTHY'.
'off' acts as a link.
(Other definitions for earthy that I've seen before include "grubby" , "Crudely uninhibited" , "Suggestive of soil" , "Gross, like the soil" , "Coarse, vulgar" .)