Hair algae is such a head ache in this hobby.
If NO3 and PO4 are reading near or close to zero, don't be fooled. The algae are taking up the nutrients already.
If your live rock is old, 2 years +, calcareous rock soaks up phosphates like a sponge over time and slowly releases them back into the water column. It's a form of old tank syndrome.
This could very well be the problem if it's not associated with an obvious source such as overfeeding, overstocked tank, etc.