Your listener.log file can get quite large if you do not make it part of your housekeeping scripts, and renaming it while the listener is running is not a good idea.

Here is the method to follow to clean it up while your listener is still running.

Log into your listener from the command prompt (make sure your Oracle environment is set to that of where the listener is started from, the commands below assume there is only one (default)  listener running ) :

$lsnrctl

..

LSNRCTL>  set log_status off
Connecting to (DESCRIPTION=(ADDRESS=(PROTOCOL=IPC)(KEY=EXTPROC)))
LISTENER parameter “log_status” set to OFF
The command completed successfully

(Now go delete/rename $ORACLE_HOME/network/log/listener.log to something else in another OS session )
LSNRCTL> set log_status on
Connecting to (DESCRIPTION=(ADDRESS=(PROTOCOL=IPC)(KEY=EXTPROC)))
LISTENER parameter “log_status” set to ON
The command completed successfully
LSNRCTL> quit