I like dunce's cap to be of remarkable quality (6)
I believe the answer is:
iconic
'be of remarkable quality' is the definition.
'i like dunce's cap' is the wordplay.
'like dunce's cap' becomes 'conic'.
'i'+'conic'='ICONIC'
'to' is the link.
(Other definitions for iconic that I've seen before include "admired type" , "that's like an emoji?" , "Culturally representative" , "Representatively symbolic" , "conventional type" .)