Time series - is it necessary to retrain the model when new time series data is present
It is good practice to retrain model once in a while. That "in a while" depends on the specific task, of course. This is due to the fact that countless unmeasurable things change continuously.

Think for example about a model to forecast companies' revenues: the rules of the game change continuously, the market today is not like the market one year ago, not to mention five years ago. This is the first example that I thought about, but it's true for pretty much any possible application of ML.

That is why it was observed that models' performance deteriorates in time. For that reason, it is good practice to keep your models updated with fresh data.