How has Kira - in Gathering Blue earned her 4 syllables?

It was because of her exceptional skill in embroidery that she was able to earn her four syllables. In the story, she was tasked to repair and embellish the Singer’s robe. It was this talent of hers that also saved her from being sent to death.

Kira earned her 4 syllables by her creative talent. She learned to sew and dye threads from her mother but she surpassed her mother's skills when she learned to mix dyes and become more creative. Her talent in embroidery led her to become a four syllable.

Under her new role as Kira the Threader, she is tasked to repair, restore, and further enhance the Singer's robe.