The ro-vibrational and pure rotational spectra of the linear ion HC3O+ have been investigated in a 4 K cryogenic ion trap instrument. For this, a novel action spectroscopic technique, called leak-out-spectroscopy (LOS, Schmid et al., J. Phys. Chem. A 2022, 126, 8111), has been utilized and characterized. In total, 45 ro-vibrational transitions within the fundamental band of the ν1 C-H stretching mode were measured with a band center at 3237.132 cm-1, as well as 34 lines from the combination band ν2 + ν4, and 41 lines tentatively identified as the combination band ν2 + ν5 + ν7, interleaved and resonant with ν1. Surprisingly, also two hot bands were detected despite the cryogenic operation temperature. Based on the novel action spectroscopy approach, a new double-resonance rotational measurement scheme was established, consisting of rotational excitation followed by vibrational excitation. Seven rotational transitions were observed between 89 and 180 GHz. Highly accurate spectroscopic parameters were extracted from a fit using all available data. In addition, a pulsed laser system has been employed to record a low resolution vibrational spectrum, in order to demonstrate the compatibility of such lasers with the LOS method.