Both observations and simulations suggest that the solar filament eruption is closely related to magnetic flux emergence. It is thought that the eruption is triggered by magnetic reconnection between the filament and the emerging flux. However, the details of such a reconnection are rarely presented. In this study, we report the detailed reconnection between a filament and its nearby emerging fields, which led to the reconfiguration and subsequent partial eruption of the filament located over the polarity inversion line of active region 12816. Before the reconnection, we observed repeated brightenings in the filament at a location that overlies a site of magnetic flux cancellation. Plasmoids form at this brightening region, and propagate bidirectionally along the filament. These indicate the tether-cutting reconnection that results in the formation and eruption of a flux rope. To the northwest of the filament, magnetic fields emerge, and reconnect with the context ones, resulting in repeated jets. Afterwards, other magnetic fields emerge near the northwestern filament endpoints, and reconnect with the filament, forming the newly reconnected filament and loops. A current sheet repeatedly occurs at the interface, with the mean temperature and emission measure of 1.7 MK and 1.1x10(28) cm(-5). Plasmoids form in the current sheet, and propagate along it and further along the newly reconnected filament and loops. The newly reconnected filament then erupts, while the unreconnected filament remains stable. We propose that besides the orientation of emerging fields, some other parameters, such as the position, distance, strength, and area, are also crucial for triggering the filament eruption.