The phrase "largest carrier" refers to the company or organization that has the most customers or transports the most people or goods. They are the biggest and most dominant in their industry. Full definition
The two firms have allegedly been in talks over a possible merger of the second - largest satellite TV operator and the fourth - largest carrier in the country. (techtimes.com)
With large carriers, miles to different locations are fixed. (valuepenguin.com)
This isn't an unusual practice as other large carriers do it as well. (johnnyjet.com)