It depends upon which part of the country you're in. In hurricane country, inspection wants to make sure your roof doesn't go flying through your neighbor's living room. The roof should probably have been incorporated into the walls at the design stage.

As @joseph corlett notes the roof probably should've been part of the design. IF the walls are sturdy enough you could have a gabled roof or shed roof. If the roof is designed to repel water and or snow it has to be even stronger. However, if it's going to have holes, slats to open air than the demand for strength wouldn't be as great. At any rate you'll probably want vertical metal ties that firmly attach the roof frame to the vertical 2 x 6's (looks like 2 x 6's).. Finally that's a pretty large area to cover for a roof over existing 3 walls and you'll have to make sure the vertical wall posts will support the weight and won't sink into the grass/ground? Also those vertical 2 by's are really far apart and usually wall studs are 16 to 24 inches apart and not (what looks like) 8 or 10 feet apart. It's a good start and looks nice but you might want to enage an architect and think about checking with neighborhood HOA?

Also consider the effect of a substantial roof on the light you get in the adjacent windows! Maybe you could use sail-type shades in the necessary seasons only...

Can we maybe see the size of this spa? I do agree the roof should have been part of the structure from the beginning and those walls are interesting since they have no support for way too many feet. Post the overhead pic here in a comment.

Build a pergola around/over it.

Get one of those retractable fabric pergolas