TaIrTe4 is an example of a candidate Weyl type-II semimetal with a minimal possible number of Weyl nodes. Four nodes are reported to exist in a single plane in k space. The existence of a conical dispersion linked toWeyl nodes has yet to be shown experimentally. Here, we use optical spectroscopy as a probe of the band structure on a low-energy scale. Studying optical conductivity allows us to probe intraband and interband transitions with zero momentum. In TaIrTe4, we observe a narrow Drude contribution and an interband conductivity that may be consistent with a tilted linear band dispersion up to 40 meV. The interband conductivity allows us to establish the effective parameters of the conical dispersion; effective velocity v = 1.1 x 10(4) m/s and tilt gamma = 0.37. The transport data, Seebeck and Hall coefficients, are qualitatively consistent with conical features in the band structure. Quantitative disagreement may be linked to the multiband nature of TaIrTe4.