Hat of one in lurid extremities (3)
I believe the answer is:
lid
'hat' is the definition.
(lid can informally mean a hat)
'one in lurid extremities' is the wordplay.
'one' becomes 'i' (Roman numeral).
'in' is an insertion indicator.
'lurid extremities' becomes 'ld' (I am not sure about this - if you are sure you should believe this answer much more).
'i' going into 'ld' is 'LID'.
'of' is the link.
Can you help me to learn more?
(Other definitions for lid that I've seen before include "Top crust of pie" , "Top or cover" , "Kind of cover, may be hinged" , "Cap or top for container" , "Hinged or removable cover as for bottle" .)