Narrow bipolar events (NBEs) are occasionally reported to occur within a few ms after Terrestrial Gamma-ray Flashes (TGFs), while the formation mechanism remains mysterious partially due to the lack of sufficient observations. Here, nine more TGFs of this scenario are reported with concurrent LF sferics and lightning location data. The gamma-ray production in these TGFs preceded the occurrence of NBEs by a minimum of 60 µs up to 13.5 ms, and no other fast leader discharge was found within 20 ms before the TGF. The TGF-preceded positive NBEs occurred at altitudes of 8.6–11 km in thunderstorms, likely in the high electric field (E-field) region of lightning initiation. The analyses show that the NBE-preceding TGFs bear harder energy spectrum with larger proportion of high-energy photons than EIP-related TGFs produced in association with lightning leader. Our findings support the relativistic feedback mechanism of gamma-ray generation in the large-scale thunderstorm E-field.