Our algorithm updates keyword data for Organic Keywords report depending on the keyword's estimated search volume, wherein the data for more popular keywords are updated more frequently.
You can read more about the search volume metric and how we at Ahrefs calculate it here: https://ahrefs.com/blog/seo-metrics/.
There is no option to initiate the update manually. We recommend using the Rank Tracker tool to see more frequent updates. In Rank Tracker, keywords will be updated weekly, every 3 days, or daily, depending on your subscription plan.
However, we are working on improving the update rate of Organic Keywords.