.........Consider a task group with a carrier, a couple of Type 23s (with Merlin and sonar 2087), and somewhere an SSN: I am leaving Maritime Patrol Aircraft out for the moment. SSN scouts ahead of a task group, Merlins fly long range sorties from the carriers (and also from the T23s), and T23s use their quiet propulsion and towed array sonar for long range detection.
Off the top of my head a Merlin has a cruising speed of 150 knots and an endurance of five hours, so can maintain station quite some distance from the high value unit (carrier, amphibious ships, important RFA, STUFT or Chartered vessels), but doing this means you need quite a few of them - hence the carrier......
So,the TF is there to defend the carrier, and the carrier is there to carry the assets to defend the TF.
Technically this is known as a self-licking lollipop......