A little surprised at Edith being given tranquillisers (7)
I believe the answer is:
sedated
'given tranquillisers' is the definition.
(tranquilisers are a sedative)
'a little surprised at edith' is the wordplay.
'a little' indicates a hidden word.
'SEDATED' can be found hidden inside 'surprised at edith'.
'being' is the link.
(Other definitions for sedated that I've seen before include "Dead set (anag) - tranquillised" , "Drugged" , "Under the influence of drugs" , "Given a tranquilliser" , "Tranquilised" .)