In terms of the climate zones that's going to be affected a lot by latitude and how big the landmasses are. So it's hard to say without a wider context or scale...
If you want more detailed climate input a few more details are needed... basically, how big is the map? And how much landmass is there not pictured off to the west? And at approximately what latitude are we at... do you have an Earth equivalent city that you would say is climactically similar to one of your settlements there that you could use to place it there?
The climate is hard to comment on because the wind directions are tricky to put together as shown it looks like you are rainshadowing from both east and west suggesting you have rain-laden winds coming from both directions....
As a general climate comment the central desert extending all the way to the south water makes less sense simply because it doesn't also extend all the way to the western mountain range... and if wet air can come from west and/or east you'd expect that lovely water-way to provide some rain to that zone
...But before I get too deep into it, it depends on how realistically you want to model the climate.
Because if you are content with just plausible, then you don't really need to worry about it because it's probably fine. I use a really simplified "realistic" climate modelling for myself and I'm sure other people here get far more into minutiae than I have the patience for, and then other maps are perfectly fine with, "I would like a desert here" because I think it fits the story I'm telling for this map or because I think it looks good