Why no new quasars? Why are there no quasars younger than 13 billion years old? I have researched the emission spectrum of quasars and found only hydrogen. Could it be that after a billion years after the Big Bang, heavier elements transformed quasars into Black Holes?
 A: Where do you get the idea that there are no quasars younger than 13 billion years old and what do you mean by the "age" of a quasar? Also the quasar phenomenon is thought to be due to the accretion of matter into supermassive black holes.
Many quasars are seen at very high redshifts of 8 or so, and therefore can be no older than a billion years. There may be a problem eventually in finding younger quasars because there must be a certain amount of time required for the supermassive black holes at their centres to grow. 
There appears to be a peak in the co-moving population density of quasars at redshifts of between 2 to 2.5. Depending on exactly which cosmological parameters one adopts, these quasars are about 5 billion years old (where age here refers to time since the big-bang). 
The nearest quasars to us are about 1 billion light years away (e.g. 3C 273, Mkn 231), but quasars appear to be getting rarer at lower redshifts, indicating that quasars are gradually "turning off".
Thus I don't know what to make of your question - quasars are apparent over a very broad range of cosmic epochs, from about 1 billion years after the big bang to about 1 billion years in the past.
