Rotating reference frames are tricky in special relativity, but that's not really relevant to the question about placing a clock or apple in circular motion. The clock moving at $0.99c$ would tick 1/7 as fast, in the lab frame. The apple would last 7 times as long. This is true regardless of whether the motion is in a straight line or a circle. The circular motion only means that the inner and outer edges of the clock/apple would age at different rates.

The premise of the question doesn't really involve rotating reference frames. The circular motion of the clock or apple can be straightforwardly analyzed in an inertial lab frame. The clock moving at $0.99c$ would tick 1/7 as fast, in the lab frame. The apple would last 7 times as long. This is true regardless of whether the motion is in a straight line or a circle. The circular motion only means that the inner and outer edges of the clock/apple would age at different rates.