Beef breakfast sausage
Professional charcutier here. We usually only make beef sausage from grass fed beef, which means our ground beef is very lean. Depending on the recipe, we have various tricks for improving the texture:


We add beef fat if available to add richness, or even pork fat if we 
don't have enough beef fat.
For a 5lb batch of ground beef for hamburgers, we'll add an egg or two and that
will give it some cohesion.
As thatdude says, cooked rice is a good way to give your sausage some
starchiness, as in boudin.
You could try mixing your sausage with heavy cream in addition to
adding eggs (as is done with traditional bratwurst)
Add about half a cup of milk powder for every 5 pounds of sausage.


Any one of the above should accomplish what you're seeking. You can even combine some methods. In our bratwurst, we add milk powder, eggs, and heavy cream. Experiment and see where your texture is after that!