How quickly could a commercial airline integrate advances in technology into its fleet?
It depends on the advance. Generally, there are three ways how airliners can be improved:


Operations and procedures: This can be as simple as faster turn-around times so aircraft will be more profitable, or as complicated as doing away with airways which would help to shorten trips, but depends on changes in regulations which have been in place for decades.
Better equipment: All parts of an aircraft are designed to be individually replaceable, and swapping old engines for newer, more fuel efficient ones will bring already two thirds of the efficiency benefits of replacing the whole aircraft. Other examples could be less heavy furnishings or more precise instruments. But there are limits, and every change needs to be approved by regulatory authorities.
Newer aircraft models: This brings aerodynamics, engines and equipment up to the status quo, and is done by airlines on a regular basis to improve both their attractiveness and their profitability. Examples are Singapore Airlines, which pride themselves on an average age of their fleet of just seven years, or Vueling, which thanks to a recent expansion has lower seat-mile cost than all their competitors.


Generally, the days of dramatic technology advances are long gone. Today, years of research are justified by single-digit percentage advances, and a new development like the A380 is started with a promise of just 15% less seat-mile cost when compared to airliners which are two decades old by the time the new plane is put into service.

To answer your question directly: Changes which produce meaningful improvements need years of preparation and testing for approval by the authorities. Quick gains are not possible anymore.