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This is implemented in SageManifolds, see for instance here for an example of vector field on the sphere S^2 (in the section "Module of vector fields" of the worksheet).
SageManifolds is not fully implemented in SageMath yet, so you have to install it according to these instructions. Note that SageManifolds is installed in the SageMathCloud (see here for some SMC example including vector vectors fields on S^2).