In "Gathering Blue," who wants to create a song for Kira?

The answer to your question lies in Chapter 18. There, we discover that Jo wants to write a new song for Kira.
In the story, Jo has been assigned to prepare for her eventual role of Singer. She is an orphan and is described as "hardly more than a toddler." However, her exceptionally beautiful voice has led to her being chosen as the next Singer. Like previous new "artists," Jo is locked in her room at night; as a Singer-in-training, she is forced to learn new songs every day. In Chapter 15, we discover that Thomas has carved a key that will unlock any door in the Edifice; this is the key he and Kira use to unlock Jo's door when they slip in to see her at night.
In Chapter 18, during a visit, Jo offers to make a new song for Kira. In reply, Kira cautions that they must be quiet on their visits so as not to alert the authorities to their nightly get-togethers. Jo understands this and maintains that, one day, when she gets the chance to, she will sing her new song for Kira "horrid loud." They both discuss the upcoming Gathering, and Jo proudly proclaims that she will be right up front during the event. The exchange ends with Jo asserting that, when she is Singer, she will be able to make her own songs again.