Priceless item in Basel damaged (11)
I believe the answer is:
inestimable
'priceless' is the definition.
(I've seen this before)
'item in basel damaged' is the wordplay.
'damaged' indicates anagramming the letters.
'item'+'in'+'basel'='iteminbasel'
'iteminbasel' anagrammed gives 'INESTIMABLE'.
(Other definitions for inestimable that I've seen before include "Not able to be measured" , "Very great" , "Priceless" , "worth a fortune" .)