In Copenhagen, cybersex is a business providing a service (6)
I believe the answer is:
agency
'a business providing a service' is the definition.
(I've seen this before)
'in copenhagen cybersex is' is the wordplay.
'in' indicates a hidden word.
'AGENCY' is hidden within 'copenhagen cybersex is'.
(Other definitions for agency that I've seen before include "Administrative unit" , "Business that acts for actors" , "Recruitment bureau" , "Government unit - business providing services" , "Business that acts for another business" .)