Thank you for your answer,
I am sure that the serial part of the MK20 is not the problem because it can do rs232 communication with others components I use. I made a diagram of how I connected my CLRC. Does this seem OK for you or did I misunderstand something in the datasheet on the RS232 connection (IF3 is connected to VDD and IFSEL pins to GND)?

Another thing that I want to verify is the frame I send. In the picture I wanted to read Command register (0x00). In yellow there is the signal in the RS232 part and in blue it is the signal between the MAX3221 and the CLRC663 plus

Does this frame seems good to you or must I send something before (it is the first time I use this component, so I don't think it is in Standby mode)?
Thank you in advance for your help.
Best regards
Mathieu