For a new face recognition system , do we need to train the network with the new dataset or we can use the model directly given in the assignment ?
This is a complicated question and there isn’t a simple “one size fits all” answer. You will probably need at least to do some additional training on your specific dataset, but exactly how you approach that requires some thought and experimentation. This is a case of “transfer learning”, of course. I suggest you start by watching Prof Ng’s lectures in that section again as he does his usual clear job of explaining the various approaches and tradeoffs.
For example, the first step is to select some images from the original training set and from your dataset and compare them. Is there anything noticeably different about your images from the earlier training set? Indoor vs outdoor (artificial vs natural light) or camera angles or … There are also questions about how many of the layers you need to train for whatever additional training you need to do. It is a hyperparameter meaning a decision you need to make whether you do the additional specific training on all the layers or only the layers after some point.
These are just a few of the considerations that Prof Ng mentions. Rather than depend on what I said, it would really be better to watch the Transfer Learning lectures again with your problem in mind.