Context.The radio source at the center of the galaxy cluster Abell 2626, also known as the Kite, stands out for its unique morphology composed of four symmetric arcs. Previous studies have probed the properties of this source at different frequencies and its interplay with the surrounding thermal plasma, but the puzzle of its origin is still unsolved.Aims.We use a new LOw-Frequency ARray (LOFAR) observation from the LOFAR Two-meter Sky Survey at 144 MHz to investigate the origin of the Kite.Methods.We present a detailed analysis of the new radio data, which we combined with archival radio and X-ray observations. We produced a new, resolved spectral index map of the source with a resolution of 7″ and we studied the spatial correlation of radio and X-ray emission to investigate the interplay between thermal and nonthermal plasma.Results.The new LOFAR data changed our view of the Kite because we discovered two steep-spectrum (α < −1.5) plumes of emission connected to the arcs. The spectral analysis shows, for the first time, a spatial trend of the spectrum along the arcs with evidence of curved synchrotron spectra and a spatial correlation with the X-ray surface brightness. On the basis of our results, we propose that the Kite was originally an X-shaped radio galaxy whose fossil radio plasma, after the end of the activity of the central active galactic nucleus, has been compressed as a consequence of motions of the thermal plasma encompassing the galaxy. The interplay between the compression and advection of the fossil plasma, with the restarting of the nuclear activity of the central galaxy, could have enhanced the radio emission of the fossil plasma producing the arcs of the Kite. We also present the first, low-frequency observation of a jellyfish galaxy in the same field, in which we detect extended, low-frequency emission without a counterpart at higher frequencies.