I do not know whether 1N NaOH is sterile or not, but the first 1N NaOH solution I used in the cell culture turned to be a little cloudy after a few days.
Xiuyue Jia, the cloudy after days is not contamination, is precipitation of Na2Co3. CO2 from atmosphere reacts with water to form H2CO3, that reacts with Na+ ions from NaOH to form Na2CO3.
You can both filter or autoclave it. If you decide to filter it, just check that your filter material is compatible with 1N NaOH. Some filters (such as some cellulose acetates) may not be compatible, decomposing and not filtering properly (or even contaminating with filter residues) your solution when filtering relative big volumes.