Yes, the chakra supply for each individual can grow through training. But will be limited by genetics.
Let's take a look at what chakra is.
Chakra is created when two other forms of energy, known collectively as one's "stamina", are molded together. ~ Naruto-wiki
With the first form being
Physical energy (身体エネルギー, shintai enerugī) and the second one being
Spiritual energy (精神エネルギー, seishin enerugī)
By training ones Physical body and Mental strength, the chakra pool can be increased.
Genetics however does play a mayor role. As some people, such as Naruto for example, just have a very large pool from the get go. And even with a lot of training, somebody like Ino would never be able to reach the same chakra pool size.
This limit is best observed with Rock Lee, as his genetics limited his growth on Spiritual energy, he tries to overcome it through Physical energy.
It is also possible to indirectly improve one's chakra pool, through Chakra control. It does not directly expand the chakra pool itself, but allows for a user to do more with the same amount of chakra.