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The star V426 Sge (HBHA~1704-05), originally classified as an emission-line object and a semi-regular variable, brightened at the beginning of August 2018, showing signatures of a symbiotic star outburst. We aim to confirm the nature of V426 Sge as a classical symbiotic star, determine the photometric ephemeris of the light minima, and suggest the path from its 1968 symbiotic nova outburst to the following 2018 Z And-type outburst. We re-constructed an historical light curve (LC) of V426 Sge from approximately the year 1900, and used original low- and high-resolution spectroscopy complemented with Swift-XRT and UVOT, optical UBVRcIc and near-infrared JHKL photometry obtained during the 2018 outburst and the following quiescence. The historical LC reveals no symbiotic-like activity from 1900 to 1967. In 1968, V426 Sge experienced a symbiotic nova outburst that ceased around 1990. From approximately 1972, a wave-like orbitally related variation with a period of $493.4\pm 0.7$ days developed in the LC. This was interrupted by a Z And-type outburst from the beginning of August 2018 to the middle of February 2019. At the maximum of the 2018 outburst, the burning white dwarf (WD) increased its temperature to $>2\times 10^5$ K, generated a luminosity of $\sim 7\times 10^{37}(d/3.3kpc)^2$ erg/s, and blew a wind at the rate of $\sim 3\times 10^{-6}$ M$_{\odot}$/yr. The donor is a normal M4-5 III giant and the accretor is a low-mass $\sim$0.5 M$_{\odot}$ WD. During the transition from the symbiotic nova outburst to the quiescent phase, a pronounced sinusoidal variation along the orbit develops in the LC of most symbiotic novae. The following eventual outburst is of Z And-type, when the accretion by the WD temporarily exceeds the upper limit of the stable burning. At this point the system becomes a classical symbiotic star.