What are some of the barriers to trading services? As I understand it countries negotiate free trade agreements in services using the WTO GATS.

But what are some of the barriers to the transnational exchange of services that an FTA would seek to address?

Surely something as ephemeral as a service can be sold across national borders easily because there are few or no physical components?
If you look at the four different ways that international service trade is categorised by the GATS, that will help you think about what sort of constraints are faced.  The four GATS "modes" are:


Cross border (the most simple): a firm in country A supplies a service to customers in country B.
Consumption abroad: someone from country B visits A and uses a service there.
Commercial presence: a firm in country A sets up a subsidiary in B to supply B's customers.
Presence of natural persons: a firm in country A moves staff to B to provide services there.


Some example constraints, by mode:


Some countries don't allow their citizens to hold accounts with foreign banks.
The US historically not allowing its citizens to visit Cuba.  (Mode 2 constraints are the rarest.)
Rules specifying that service companies must be 51% owned by locals have been common in various countries.
All immigration law places restrictions on this.