Belive urchins, sea hares and maybe Tangs, rabbit fish, etc depending on your tank size and abilities.
I had some of that brown algae after my cycle and my tomini tang would pluck it off the rocks so it could float and go into the overflow and sometimes I saw him actually pull of longer 1/2 strands and eat it but tended to prefer the shorter strands by far.
Your pic is hard to see but mine was actually a green hair algae that slowly started to turn to a tan/brown color before gradually going away. I also used a toothbrush a few times to help manually remove some and noticed the better the water parameters helped some of it to come off fairly easy and much easier to do before lots of corals were started but not sure if you have that option.