Third-degree deprivation of lustre (5)
I believe the answer is:
gloss
'lustre' is the definition.
(I've seen this before)
'third-degree deprivation' is the wordplay.
'third-degree' becomes 'g' (3rd letter of 'degree').
'deprivation' becomes 'loss' (synonyms).
'g'+'loss'='GLOSS'
'of' is the link.
(Other definitions for gloss that I've seen before include "Very shiny finish" , "Polish - explanatory comment" , "Superficial appearance" , "Shiny type of paint" , "Render plausible" .)