In what manner does it "not work"? Be specific.

"what kind of shell are you using?" "unix"
"what kind of car are you driving?" "blue"

UNIX has many shells, "UNIX shell" tells us nothing.

Code:

function newrecord () {
clear
read -p "please enter a user number: " users2

If you're not using BASH, read -p won't work or won't do what you expect -- -p means read from a coprocess in ksh for instance, and other shells won't have it at all.

Code:

output=$(grep "$users2" appraisalrecord)

What's in appraisalrecord?

Code:

output1=$(echo $users2 | tr -dc '[:digit:]')

This is to remove everything except digits I take it?

Code:

if [[ -n "$output" ]]; then
echo -e "The ID has already been taken\n"
sleep 2
newrecord
fi

Why is newrecord calling itself? This will be a recursion. And the existing call to newrecord won't end, potentially making it an infinite recursion. You should have a loop outside newrecord that keeps calling it in a loop if you want it to happen more than once.

Instead of checking the output of grep, why not check grep's return value? it returns nonzero when nothing's found, and zero when it's found, so:

Code:

if grep -q "$users2" appraisalrecord
then
        echo "The ID has already been taken"
        echo
...

Code:

if [[ $users2 = $output1 ]]; then

This will blow up whenever users2 or output1 are blank, put quotes around them.