Postbag has Theresa somewhat horrified (6)
I believe the answer is:
aghast
'horrified' is the definition.
(thesaurus)
'postbag has theresa somewhat' is the wordplay.
'somewhat' indicates a hidden word.
'AGHAST' is hidden in the letters of 'postbag has theresa'.
(Other definitions for aghast that I've seen before include "Stupefied with horrer" , "What's carried in bag has teacher" , "'Horrified, shocked (6)'" , "Filled with consternation or horror" , "Horrified, filled iwth consternation" .)