There are a couple of things that happened to the Latin alphabet during the Old Latin Period.
1. Letter K was given a lower standing compared to C. Letter C now stood for both sounds "G" and "K". It was used very rarely, in a small number of Greek borrowed words (mostly loan words), such as "Kalendae", often interchangeably with C.
2. Possibly during the 3rd century BC, letter Z was dropped, most likely because it was unneeded to write Latin proper.
3. The newly invented letter G, a C modified with a small horizontal stroke, was added into the Latin alphabet.
Letter C = voiceless stop consonant (plosive) sound /k/.
Letter G = voiced stop consonant (plosive) sound /g/.
As a result, the Old Latin Alphabet contained 21 letters:
Emperor Claudius made an attempt to introduce three additional letters. The effect of this was short-lived.
However, after the Roman conquest of Greece in the 1st century BC:
1. Letter Y was adopted from the Greek language and placed at the end of the Latin alphabet.
2. Letter Z was readopted from the Greek and placed right after Y.
As a result, Classical Latin alphabet contained 23 letters:
During the Late Antiquity, with the expansion of the Roman Empire, the Latin alphabet spread from Italy to the lands surrounding the Mediterranean Sea.
The Eastern Roman Empire (Greece, Asia Minor, the Levant and Egypt) kept Greek as a lingua franca among themselves.
The Western Roman Empire spoke Latin. Thus, the western Romance languages (French, Italian, Portuguese and Spanish), as they evolved out of Latin, continued to use and develop the Latin alphabet.