To enter Operation FS, Second Operation SN and it's corresponding quests need to be cleared first.
Operation FS consists of E-6 and E-7. E-6 will allow you to use a battle force active in Second South Pacific Battle (E-3), which is mainly composed of a Carrier Task Force. E-7 will allow you to use all the forces over Solomon (except E-5 fleets).
You can obtain Libeccio in expanded operation over the west (E-5), Kazagumo in Operation FS (E-6/7), and after completing the whole event, Teruzuki.
"... and after completing the whole event, Teruzuki" makes it sound like once the event is cleared, she'll start dropping. "...by clearing the event" would be more clear if you want to say she's the reward for clearing E-7