Beginning to hail carriage, figure lifted headwear (7)
I believe the answer is:
hairnet
'headwear' is the definition.
(I know that hairnet is a type of headwear)
'beginning to hail carriage figure lifted' is the wordplay.
'beginning to' suggests taking the first letters.
'carriage' becomes 'air' (both can mean someone's stance or posture).
'figure' becomes 'ten' (I've seen this before).
'lifted' says the letters should be written backwards (going up in down clue).
The initial letter of 'hail' is 'h'.
'ten' in reverse letter order is 'net'.
'h'+'air'+'net'='HAIRNET'
(Other definitions for hairnet that I've seen before include "Cover for head" , "protection overhead" , "Lock-keeper" , "It protects locks" , "The rain (anag) - used after shampooing?" .)