Nose pierced by third ring and nose without ring — foolishness (8)
I believe the answer is:
nonsense
'foolishness' is the definition.
(I've seen this before)
'nose pierced by third ring and nose without ring' is the wordplay.
'pierced by' means one lot of letters goes inside another.
'third ring' becomes 'n' (3rd letter of 'ring').
'and' means one lot of letters go next to another.
'without' is a deletion indicator.
'ring' becomes 'o'.
'nose' with 'o' taken away is 'nse'.
'nose' placed around 'n' is 'nonse'.
'nonse'+'nse'='NONSENSE'
(Other definitions for nonsense that I've seen before include "Bunk" , "Rubbish, twaddle" , "Boloney, tosh" , "Gobbledegook" , "Farce" .)