On the contrary, in Connemara it might be worn as headgear (5)
I believe the answer is:
tiara
'headgear' is the definition.
(tiara is a kind of headgear)
'on the contrary in connemara it might' is the wordplay.
'on the contrary' says the letters should be written backwards (letters in the opposite or contrary direction).
'in' indicates the answer is hidden within the clue.
'arait' is hidden in the letters of 'connemara it might'.
'arait' written backwards gives 'TIARA'.
'be worn as' is the link.
This may not be right. Some or all of it may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for tiara that I've seen before include "Half a crown!" , "expensive headwear" , "Type of diadem" , "special headgear" , "Ornamental head gear" .)