single word for improving little by little

Solution 1:

I need to tweak your example a little, and phrase it as:

If you practice guitar everyday, your skills will grow incrementally, and you will eventually become a master.

The key missing word here is incrementally, using this definition from M-W:

of, relating to, being, or occurring in especially small increments <incremental additions> <incremental change>

Solution 2:

Progress?

to grow or develop, as in complexity, scope, or severity; advance:
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If you practice guitar everyday you will progress, and eventually be a master.

In your example, however, I would use improve.

If you practice guitar everyday you will improve, and eventually be a master.