Background: The direction of an axial vector (which is related to rotational motion) is perpendicular to the plane containing the vectors which are being cross multiplied in a direction in which thumb points when the fingers are curled from the first cross multiplicand to the second cross multiplicand through the smaller angle (Right Hand Rule). Thus the direction of cross product encodes the orientation of the axis of rotation as well as the sense of rotation. But my book says that the sense of rotation of an axial vector like torque is indicated by a - or a + sign before its magnitude, i.e, negative torque indicates that the sense of rotation is clockwise whereas positive torque indicates that the sense of rotation is anticlockwise.
My Question: Is it necessary to indicate the sense of rotation separately as it is already encoded in the direction of the axial vector which is determined by the right hand rule?
I think the answer to your question is "it depends on the context".
If the text is mathematical and the torque is clearly just the cross product of the lever arm and the force then the sense of rotation is indeed determined.
If the text is about a (physical) system where you are told the axis of rotation (perhaps it's the $z$-axis) then to know the torque you need both its absolute magnitude and its direction. You can't specify the direction with a $+$ or $-$ sign or call it "clockwise" or "counterclockwise" until you've specified a convention (essentially equivalent to the right hand rule). Try to look back in "your book" to find out where this is explained.