Cover head around capital of Libya (5)
I believe the answer is:
plate
'cover' is the definition.
(thesaurus)
'head around capital of libya' is the wordplay.
'head' becomes 'pate' (I've seen this before).
'around' means one lot of letters goes inside another.
'capital of' suggests taking the first letters.
The initial letter of 'libya' is 'l'.
'pate' going around 'l' is 'PLATE'.
(Other definitions for plate that I've seen before include "Flower" , "Flat dish for food" , "Item of crockery" , "South American river" , "trophy" .)