You may easily upgrade/downgrade your Ahrefs subscription anytime from 'Subscription Plan':
Or 'Pricing' pages:
When upgrading your plan to a higher package, changes take effect instantly. You are issued a pro-rated refund for your previous subscription and charged for a new one.
Please, mind that in this case your billing cycle dates do not change.
When downgrading your plan, no refund is issued. Changes take effect at the end of a paid period (you remain on your current plan till your next billing date).
This procedure will work for switching from monthly to monthly, as well as from yearly to yearly subscriptions.