Você quase tem, você pode tentar isto:
#!/bin/ksh -
## $1 = Folder
cd -P -- "$1" || exit
F1="TEST_FILE"
COUNT=$(($(wc -l < output.txt))) || exit
DATE=$(date "+%Y%m%d")
EXTENSION="_01_01.txt"
FILENAME="${F1}_${COUNT}_${DATE}_${EXTENSION}"
cp output.txt "$FILENAME"
Command substitution allows the output of a command to be substituted in place of the command name itself. Command substitution shall occur when the command is enclosed as follows:
$(command)
Como @don_crissti disse, leia mais em aqui