An accompanying person in Paris is stifling exclamation of surprise (6)
I believe the answer is:
escort
'an accompanying person' is the definition.
(someone who accompanies someone else)
'in paris is stifling exclamation of surprise' is the wordplay.
'in paris is' becomes 'est' ('is' in French).
'stifling' indicates putting letters inside.
'exclamation of surprise' becomes 'cor' (expression of surprise).
'est' enclosing 'cor' is 'ESCORT'.
(Other definitions for escort that I've seen before include "Custodian" , "conduct" , "Companion in corset, perhaps military" , "Act as companion, attend" , "Bodyguard" .)