Surrey’s opener doesn’t have trousers! (6)
I believe the answer is:
slacks
'trousers' is the definition.
(type of trousers)
'surrey's opener doesn't have' is the wordplay.
'opener' says to take the initial letters.
'doesn't have' becomes 'lacks' (lacking something means not having it).
The first letter of 'surrey' is 's'.
's'+'lacks'='SLACKS'
(Other definitions for slacks that I've seen before include "Avoids work - trousers" , "Pants for casual wear" , "Things to wear" , "Works lazily; trousers" , "Loose casual trousers" .)