The pronunciation of Α/α when used as a single vowel has changed almost not at all. From Classical Greek to today, the pronunciation has remained /a/ as in father, bother, cot, and top.
Here are a few names from the Hellenistic period with this vowel: Ἀβραάμ, Ἀδάμ, ᾽Αριάδνη.
When followed by the vowel ι, however, the pronunciation has changed considerably. While by the middle of the Classical period the combination αι was frequently pronounced as a diphthong similar to the vowel in white, stripe, and nigh, by the end of the Hellenistic period this combination had become a digraph, representing a single vowel sound similar to the one in set, peg, and step. This change is demonstrated by frequent confusion between αι and ε in manuscripts from this period.
Here are a few examples of words found in Hellenistic texts with αι: αἰτέω, αἰών, αἷμα.