We present the results from a dense multwavelength [optical/UV, near-infrared (IR), and X-ray] follow-up campaign of the nuclear transient AT 2017gge, covering a total of 1698 d from the transient's discovery. The bolometric light curve, the blackbody temperature and radius, the broad H and He i lambda 5876 emission lines and their evolution with time, are all consistent with a tidal disruption event (TDE) nature. A soft X-ray flare is detected with a delay of similar to 200 d with respect to the optical/UV peak and it is rapidly followed by the emergence of a broad He ii lambda 4686 and by a number of long-lasting high ionization coronal emission lines. This indicate a clear connection between a TDE flare and the appearance of extreme coronal line emission (ECLEs). An IR echo, resulting from dust re-radiation of the optical/UV TDE light is observed after the X-ray flare and the associated near-IR spectra show a transient broad feature in correspondence of the He i lambda 10830 and, for the first time in a TDE, a transient high-ionization coronal NIR line (the [Fe xiii] lambda 10798) is also detected. The data are well explained by a scenario in which a TDE occurs in a gas-and-dust rich environment and its optical/UV, soft X-ray, and IR emission have different origins and locations. The optical emission may be produced by stellar debris stream collisions prior to the accretion disc formation, which is instead responsible for the soft X-ray flare, emitted after the end of the circularization process.