Nurse visibly embarrassed about drug offered (8)
I believe the answer is:
tendered
'offered' is the definition.
('tender' can be a synonym of 'offer')
'nurse visibly embarrassed about drug' is the wordplay.
'nurse' becomes 'tend' (I've seen this before**).
'visibly embarrassed' becomes 'red'.
'about' says to put letters next to each other.
'drug' becomes 'e' (e is another name for ecstasy).
'red' put after 'e' is 'ered'.
'tend'+'ered'='TENDERED'
(Other definitions for tendered that I've seen before include "submitted" , "Offered for payment" , "Made an offer" , "Offered as at auction" , "Put in a bid for a contract" .)