American wearing hat over face (4)
I believe the answer is:
dial
'face' is the definition.
(face of a clock)
'american wearing hat over' is the wordplay.
'american' becomes 'a' (common abbreviation - e.g. in organisation names).
'wearing' means one lot of letters goes inside another.
'hat' becomes 'lid' (lid can informally mean a hat).
'over' shows that the letters should be reversed in order.
'a' inserted within 'lid' is 'laid'.
'laid' reversed gives 'DIAL'.
(Other definitions for dial that I've seen before include "Clock face" , "Face with numbers" , "Ring the clock-face" , "Indicator" , "Calibrated disc etc" .)