The effect of polymer additives on the global entrainment of a turbulent round jet was found to show two distinct regimes: the reduction and enhancement regimes in the near and far fields, respectively. Using time-resolved simultaneous particle image velocimetry and laser-induced fluorescence measurements, we hereby present an experimental study on the local entrainment and engulfment process along the turbulent/non-turbulent interface (TNTI). We find that the local entrainment velocity is augmented in both regimes, due to the contribution from polymer elastic stress and a higher probability for TNTI to visit jet centreline region where the entrainment velocity is larger. In the entrainment reduction regime, the fractal dimension and length of TNTI are smaller compared to the Newtonian case; while those in the enhancement regime are nearly not changed. The difference between the two regimes results from the fact the jet flow decays in the streamwise direction. In the near field, the flow is intense enough to substantially stretch polymers, which results in a redistribution of energy among different scales and a steeper decay of energy in the inertial range. However, in the far field, the stretching of the polymer and in turn the feedback of polymers is not strong enough to alter the inertial range scaling of the energy spectrum. Moreover, our study reveals although more ambient fluid is engulfed into the turbulent region due to the augmented large scale motion by polymers, engulfment is still not the major contribution to the entrainment in polymer-laden jet, which is similar to the case in Newtonian jet.