Perhaps something along these lines:
With[{r = Sqrt[x^2 + y^2], \[Phi] = ArcTan[x, y]},
Show[ContourPlot3D[
Evaluate[{r^2 + z^2 - 1 == 0, r == Simplify[Sin[\[Phi]]]}], {x, -1,
1}, {y, -1, 1}, {z, -1, 1}, ContourStyle -> Opacity[0.3],
AxesLabel -> {"x-axis", "y-axis", "z-axis"}, MeshFunctions -> {},
LabelStyle -> Directive[Bold, Medium, Red]],
VectorPlot3D[{Grad[r^2 + z^2 - 1, {x, y, z}],
Grad[r - Simplify@Sin[\[Phi]], {x, y, z}]}, {x, -1, 1}, {y, -1,
1}, {z, -1, 1}]]]