Anxiety as adult's lost hair (6)
I believe the answer is:
stress
'anxiety' is the definition.
(anxiety is stress or tension)
'as adult's lost hair' is the wordplay.
'adult' becomes 'a' (abbreviation).
'lost' suggests deleting specific letters.
'hair' becomes 'tress' (tress is a kind of hair).
'as' with 'a' taken out is 's'.
's'+'tress'='STRESS'
(Other definitions for stress that I've seen before include "Emotional tension" , "Pressure or strain" , "Dwell on" , "Emphasise the strain" , "'Worry, pressure (6)'" .)