Again, we can't tell you whether or not your Quaker's beak is "overgrown" without seeing a photo of it. Usually in the case of a "rescue" parrot, any species, where the beak is actually overgrown, as in "too long", it's due to the bird being fed a diet that is high in fat it's entire life, typically a cheap seed-mix. The cheap seed-mixes for small to medium sized parrots usually contain very fatty seeds such as sunflower seeds, millet, etc. And when the bird is fed nothing but a seed-mix that is high in fat, over time this fat accumulates in their liver, and causes a condition called Fatty Liver Disease. And usually the very first visual sign of a bird having Fatty Liver Disease is an overgrown beak. Since you rescued your Quaker from a neglectful home, my assumption is that he was most-likely fed nothing but a cheap seed-mix that was high in fat, as it's extremely common. And even if his beak is not actually overgrown at this point, chances are that he still has the start of Fatty Liver Disease if he has eaten nothing but a cheap seed-mix his entire life...
If you post a photo of his beak from a couple of different angles, we can tell you our opinions on whether or not it is actually overgrown and needs to be trimmed. But if it is, you'll need to find a Certified Avian Vet to not only do the trimming, but to also do a routine blood-work panel to test his liver and kidney functions to confirm or rule-out Fatty Liver Disease. There are things you can do to help reverse the Fatty Liver Disease, supplements you can start giving him every day, such as Milk Thistle, that will help to reverse the liver damage. But first you need to confirm the diagnosis, because as mentioned above there are some much more serious and life-threatening conditions that can also cause their beaks to overgrow...
Either way, an overgrown beak can eventually cause them issues with eating, so it is something that you need to get looked at ASAP...
