Can I change the hard drive of my Mac to increase the storage?

if you are running low on space, the most cost effective way to increase storage is to purchase an external HDD or SSD of sufficient capacity and move your larger files (videos, pictures, documents, etc...) to it. once they are on the EHD, you can simply erase the same files from your internal drive. and, if it's just going to be used for storage, you can use an HDD and save a few bucks over the cost of an SSD. FWIW, i personally keep very little on my internal drive.

Please identify your specific MacBook Air model: Identify your MacBook Air model - Apple Support