Very-high-energy $\gamma$-ray emission provides constraints on the morphology and the physics mechanisms involved in the evolution of pulsar wind nebulae (PWNe). In the Galactic plane, around $312 ^{\circ}$ of Galactic longitude, a promising region two-degree wide containing five powerful pulsars may offer a new insight on the transition between TeV-emitting PWNe and pulsar halos. Their rotational energies range from $10^{35}$ to $10^{37}$ erg s$^{-1}$ for ages between $13.6$ and $62.8$ kyr. Extended emission is detected with H.E.S.S. (High Energy Stereoscopic System) in their vicinity, notably around the pulsar PSR J1413-6205.

We processed $124$ hours of H.E.S.S observations with an algorithm improving background fitting for the study of extended sources. We applied a three-dimensional likelihood analysis technique to model the different sources in the region using a configuration that optimizes the collection area at the highest energies.

This contribution focuses on the detection of a new extended source around PSR J1413-6205 over 5$\sigma$ with a hard spectrum. Preliminary results on this source show a radius of $0.12 ^{\circ}$ $\pm$ $0.01 ^{\circ}_{\rm stat}$, an index of $2.06$ $\pm$ $0.20_{\rm stat}$ and a lower limit on a cut-off energy of $17$ TeV, at a $90\%$ confidence level. The detected emission is consistent with previous PWN models.