Tight-lipped, showing sensitivity about one ashes vase (8)
I believe the answer is:
taciturn
'tight-lipped' is the definition.
(thesaurus)
'sensitivity about one ashes vase' is the wordplay.
'sensitivity' becomes 'tact' (I've seen this before).
'about' is an insertion indicator.
'one' becomes 'i' (Roman numeral).
'ashes vase' becomes 'urn' (I've seen this before).
'tact' placed around 'i' is 'tacit'.
'tacit'+'urn'='TACITURN'
'showing' acts as a link.
(Other definitions for taciturn that I've seen before include "withdrawn" , "Reticent" , "Uncommunicative, of few words" , "Untalkative" , "Aloof" .)