Slice the fennel into thin shavings using a mandoline.
Cut the bottom and top off the grapefruit. Cut the peel off the sides, following the curve of the grapefruit and being careful to cut away only the peel and bitter pith. Hold the fruit in one hand over a bowl and cut the flesh of the grapefruit away from the membrane to release a wedge. Repeat until all segments are released.
Heat a large frying pan over a medium heat and coat it with extra-virgin olive oil. Add the shaved fennel. Season with salt and saute until the fennel is warm and coated with the oil, 1 to 2 minutes. Remove from the heat. Toss in the grapefruit segments, grapefruit juice and olive slivers; sprinkle with the fennel fronds. Serve immediately.