Handling of UART Errors
These errors can't be fixed, so retransmission is required. This needs some protocol at a higher level than the UART; you'll typically want to acknowledge the correct reception of a packet of data. This packet may be 1 byte, but also longer packets can be used if the communication has little errors. Acknowledge each packet by sending an ACK to the transmitter, a NACK if an error has occurred. In the latter case discard the packet and wait for retransmission.
If you use packet transfers you may want to consider CRC error checking instead of parity, which isn't very efficient (adds 1 bit per byte) and only catches single bit errors.