저번: last time

~에 이어서: in continuation from

Combined, these two words therefore mean something like:

Just like last time (in continuation from last time; this time again; again), he/she speaks Korean like a native speaker.

If I literally translate the phrase in English, it would be "to be continued from the last time". However, if I translate the whole sentence. I would probably say, He/She speaks Korean very well continuously.

저번: last time ~에 이어서: in continuation from Combined, these two words therefore mean something like: Just like last time (in continuation from last time; this time again; again), he/she speaks very good Korean.