Climate of coastal mountains

[Moros]

(this is my first time on this part of the forums or attaching an image, sorry if I post this in the wrong place or something)
For my first map I already have some ideas about what I want it to geographically be like, but I just drew this in like three seconds in Inkscape (hence the poor quality). I am make it more or less realistic in it's climate, so I made this briefly outlining some of the climate and how I got it. First off this is in the northern hemisphere, in the east of the continent I am drawing. I don't know too much about how ocean currents or mountains affect climate, but I do some, which is why I am somewhat unsure of it and asking here for opinions. My reasoning here is that as the (clockwise) currents hit the land, it runs into the mountains (which are more dense than depicted). Because of this the maritime tropical air cools down, releasing all of its water, causing relatively flooded areas in front of the mountains, and a very dry area behind (the desert). Is this a realistic scenario? If not, how do should I change it to simulate realistic conditions that would cause a desert in the east to form (I know that most deserts form in the west in the real world due to the higher presence of polar ocean currents)?
Thanks,
Moros

[Azélor]

Putting a mountain chain on the east coast is going to block the moisture it it's high enough and cover a long distance.
If not, you could still have a monsoon where wind blow not according to the usual pattern but flowing to the interior on the continent.

Also, depending on you latitude you might need another mountain chain in the west to block the moisture. But you don't need to if there is a cold current.

[AEB]

Looking at your sketch the coastal mountains look very much like the Sarawat Mountains which are situated at the Eastern End of the Arabian Peninsula in Yemen.

These mountains have an interesting climate due to the Monsoons coming off the Indian Ocean. They also contribute to the dry nature of the Arabian Peninsula due to rain shadowing.

Maybe use these mountains as inspiration?