The TE bit of SC13 register is provided to control the transmission, so please confirm the status of the TE bit.
If you want to check the status where the transmission is already completed, this can be made easily with TEND. During transmission, TEND is cleared to 0, and at the moment transmission is completed, set to 1. Immediately you write transmission data on TRD, TDRE is set to 1 to show that TDR is empty. When you transmit continuously, confirm TDRE=1 and then write transmission data.