federal laws currently governing firearms are listed in the US Code in Title 18 Chapter 44. this chapter is divided into sections (921-931) governing unlawful acts, licensing, and penalties.
The proposed gun control bill seeks to amend the current gun control laws by adding a whole new section (932)
Here is a link to the current Chapter 44.

https://uscode.house.gov/browse/prelim@title18/part1/chapter44&edition=prelim