Is ISL used for TV carriers?
The information I found is that it is used for IP connectivity. I did not find any information on TV broadcast.
If not, what are the applications of ISL?
Television broadcasts will not (generally) use ISL. The ground stations transmit signals to the satellites which they rebroadcast back to Earth.
The uplink dish is pointed toward a specific satellite and the uplinked signals are transmitted within a specific frequency range, so as to be received by one of the transponders tuned to that frequency range aboard that satellite.1 The transponder then converts the signals to Ku band, a process known as "translation," and transmits them back to earth to be received by home satellite stations.
In the case of TV broadcast the source (the ground stations) and the recipients (the large number of customers in the area the satellite broadcasts to) are both prearranged so the satellites and ground stations are placed in the correct orbits and locations to reach these areas.
ISL becomes more useful when the locations of the sender and receiver do not permit them to see the same satellite in the sky. But this does not (generally) happen in TV broadcast because the broadcaster has the ability to build a new ground station if needed.
As for what ISL is actually used for? I'm not sure. But situations such as a spy satellite on the other side of the globe seem more likely.