  We investigate the iron-based superconductor Ba$_{1-x}$K$_x$Fe$_2$As$_2$
using intense terahertz (THz) light. In the superconducting state a THz Kerr
signal is observed and assigned to non-linear THz coupling to superconducting
degrees of freedom. The polarization dependence of the THz Kerr signal is
remarkably sensitive to the coexistence of a nematic order. In the absence of
nematic order the $C_4$ symmetric polarization dependence of the THz Kerr
signal is consistent with a coupling to the Higgs amplitude mode of the
superconducting condensate. In the coexisting nematic and superconducting state
the signal becomes purely nematic with a vanishing $C_4$ symmetric component,
signaling the emergence of a new superconducting collective mode activated by
nematicity.
