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The fast growth of supermassive black holes and their feedback to the host galaxies play an important role in regulating the evolution of galaxies, especially in the early Universe. However, due to cosmological dimming and the limited angular resolution of most observations, it is difficult to resolve the feedback from the active galactic nuclei (AGNs) to their host galaxies. Gravitational lensing, for its magnification, provides a powerful tool to spatially differentiate emission originating from AGN and host galaxy at high-redshifts. Here, we report a discovery of a jet-like radio structure in a strongly lensed starburst quasar, H1413+117 or Cloverleaf at redshift z  = 2.56, based on observational data at optical, submillimetre, and radio wavelengths. With both parametric and non-parametric lens models and with reconstructed images in the source plane, we find a well-separated, kpc-scaled, single-sided radio jet located at projected |${\sim }1.2\, \mathrm{kpc}$| to the north-west of the host galaxy in the source plane. This could indicate the co-existence of feedback from the AGN by both wind and jet in the Cloverleaf quasar. [ABSTRACT FROM AUTHOR]