We (family of four) use the pulp in one of our all-time favorite meals, which we call "whatever burgers" (they are essentially veggie burgers)... we're big lentil eaters, so we take the pulp, any leftover lentils from a day or two before (or if we are really craving whatever burgers, we'll make lentils especially- most kinds work well, and canned is also fine), a few handfuls of rolled oats to bind everything, a chopped yellow onion or two for flavor, sometimes some grated ginger, a sprinkling of salt, some chopped cilantro/coriander, a chopped green chile pepper, and some dry spices (usually Indian spices- garam masala, amchur)... mix it all together, add oats until it all comes together, and saute / very lightly pan-fry in olive oil (I usually just put enough olive oil down to coat the pan, and then again before flipping). These little burgers are so healthy, addictive, and have been a hit with everyone we've served them to! Plus- great way to get the fiber we miss by juicing. (We use a mix of veggie/fruit pulp- our standard juice is kale/greens+a small apple+half a lemon+a small chunk of ginger... sometimes carrots or celery make their way in there. No one minds finding the occasional apple peel in their whatever burgers- it's all part of the whatever!)
I juice all the veggies first and then save the pulp and make turkey/veggie burgers with it. Just freeze the veggie pulp until you have enough and then buy some ground turkey and make patties and throw them back in your freezer for the future! They are so fresh tasting! I compost the fruit pulp.
Assuming you don't allow the pulp from different produce to mix, you can scoop it out and use it in broths or baking recipes. Carrot pulp especially rehydrates well in soup or in carrot cakes. Berry pulp is decent over ice cream or on toast if you have enough of it, likewise with apple if you don't mind eating skin pieces. Otherwise, compost or discard it.
We tried using some of it in soup but didn't care for the flavor as we usually have fruits and vegetables combined. So we just throw it away now. We put a gallon sized baggie in the receptacle before juicing which makes disposal a breeze. If you garden, I understand it is great to add to your compost.
I keep a compost heap so most of the time I just dump it in there. If I think ahead, I juice the vegetables first and dump that pulp into whatever soup or sauce I make next. The pulp keeps a day or two in the fridge if you wrap it up and it makes veggie soup or tomato sauce thicker.