There is no need to integrate them. Tor has its own search radar and tracking radar and missiles in one vehicle. For self defence there no need of more.
Well there is really.
You can't just take a TOR battery and sit them on the deck of a carrier and expect them to operate normally... there will be issues with parts of the ships structure causing blind spots and of course the radars of the TOR vehicles effecting and being effected by the ships various radar and ESM and ECM equipment and navigation systems too.
The Russians have developed a small deck mounted system with vertically mounted ready to fire missiles and a tracking radar... sitting those on the deck tied down with cables so you can remove them if you like... connect them to the local power so they are always ready and don't need to run generators to be ready, and also connect them to the information feed of the main ships search radar which should offer better performance than any system mounted on a vehicle, so the deck mounted systems just need to point their tracking radars in the suitable direction and scan for targets and then launch a missile which the tracking radar directs to impact.
Having four of these deck mounted trailers would allow most directions to be covered at one time and you could have half a dozen extra mounts that are cheaper and have no radar at all... they just contain 12 or 24 ready to launch missiles to be guided by one of the deck mounted trailers with a tracking radar.
There will be lots of places on deck where you wont be using at any time and if you need that space undo the cable and roll it out of the way... if it is quiet take it below deck and push it into a corner... or attach a towing vehicle and put it on a landing boat and deliver it to shore to operate with a TOR battery on land to defend forces during the landing...
This system made of manpad is totally useless. I would fear in danger if this was the only air defence system protecting my ship.
Old TOR is a capable system with a 12km range and decent accuracy able to take out enemy weapons in flight as well as aircraft... the new model has smaller faster longer ranged missiles that can be carried in double the numbers with all the weapons ready to fire in vertical launch tubes able to fly off in any direction needed... they are an excellent system... the new ones can reach 20km range and 15km altitude.
Keep in mind that this is a helicopter carrier so it will be operating with a few destroyers and perhaps cruisers so it wont be fighting the enemy on its own... even the Ka-52 attack helo it carries has an AESA radar and can use R-77 AAMs if needed.
Would like to see Turkey sending all their nastiest terrorists from Idlib and elsewhere to fight and hopefully die in Libya, it would be the best result all round... they can just send the terrorists and leave the Turkish soldiers offshore in a standoff support role...