American engaged in most of superficial beauty treatment (6)
I believe the answer is:
Here is my best explanation:
'beauty treatment' is the definition.
(I've seen this before)
'american engaged in most of superficial' is the subsidiary indication.
'american' becomes 'a' (common abbreviation - e.g. in organisation names).
'engaged in' indicates putting letters inside.
'most of' means to remove the last letter.
'superficial' becomes 'facile' ('facile' can be similar in meaning to 'superficial').
'facile' with its last letter taken off is 'facil'.
'a' put into 'facil' is 'facial'.
(Other definitions for facial that I've seen before include "Beauty treatment for front of head", "Beauty treatment for the visage", "Beauty treatment, maybe mudpack", "Type of beauty treatment" and "Cosmetic treatment".)