I want to rename files in order of file-date; from example:
file_1.pdf
file_2.pdf
to:
file_1_ONE.pdf
file_2._TWO.pdf
The script must rename the first file to "ONE" ordered by file-date.
Using the zsh shell and the number utility found in /usr/games on some BSD systems (on e.g. Ubuntu systems, this would be available from the bsdgames package):
number=1
for file in ./file_*.pdf(.Om); do
    mv "$file" "${file%.pdf}_$(number -l "$number" | tr '[:lower:]' '[:upper:]').pdf"
    number=$(( number + 1 ))
done
The (.Om) is a modifier to the preceding pattern that is specific to the zsh shell.  It makes the pattern expand to a list of filenames of regular files that is ordered by the mtime timestamp (last modified time) with the oldest file first.
The command number -l "$number" | tr '[:lower:]' '[:upper:]' would call number with the current value of $number and would return the English word corresponding to this in upper case, e.g. ONE, TWO, THREE etc.  This would be prepended with the filename without its filename suffix and with an underscore, and the string .pdf would be added to the end.
Alternatively, to avoid tr:
number=1
for file in ./file_*.pdf(.Om); do
    en_number=$(number -l "$number")
    mv "$file" "${file%.pdf}_${en_number:u}.pdf"
    number=$(( number + 1 ))
done
${en_number:u} would convert $en_number (the output from number) to upper case.  The :u modifier is zsh-specific and ${variable:u} corresponds to ${variable^^} in bash.
Testing:
$ for name in file_{1..10}.pdf; do touch "$name"; sleep 2; done
$ ls -lt
total 4
-rw-r--r--  1 kk  wheel    0 Jan 31 13:28 file_10.pdf
-rw-r--r--  1 kk  wheel    0 Jan 31 13:28 file_9.pdf
-rw-r--r--  1 kk  wheel    0 Jan 31 13:28 file_8.pdf
-rw-r--r--  1 kk  wheel    0 Jan 31 13:28 file_7.pdf
-rw-r--r--  1 kk  wheel    0 Jan 31 13:28 file_6.pdf
-rw-r--r--  1 kk  wheel    0 Jan 31 13:28 file_5.pdf
-rw-r--r--  1 kk  wheel    0 Jan 31 13:28 file_4.pdf
-rw-r--r--  1 kk  wheel    0 Jan 31 13:28 file_3.pdf
-rw-r--r--  1 kk  wheel    0 Jan 31 13:28 file_2.pdf
-rw-r--r--  1 kk  wheel    0 Jan 31 13:28 file_1.pdf
-rw-r--r--  1 kk  wheel  163 Jan 31 13:26 script.sh
$ zsh script.sh
$ ls -lt
total 4
-rw-r--r--  1 kk  wheel    0 Jan 31 13:28 file_10_TEN.pdf
-rw-r--r--  1 kk  wheel    0 Jan 31 13:28 file_9_NINE.pdf
-rw-r--r--  1 kk  wheel    0 Jan 31 13:28 file_8_EIGHT.pdf
-rw-r--r--  1 kk  wheel    0 Jan 31 13:28 file_7_SEVEN.pdf
-rw-r--r--  1 kk  wheel    0 Jan 31 13:28 file_6_SIX.pdf
-rw-r--r--  1 kk  wheel    0 Jan 31 13:28 file_5_FIVE.pdf
-rw-r--r--  1 kk  wheel    0 Jan 31 13:28 file_4_FOUR.pdf
-rw-r--r--  1 kk  wheel    0 Jan 31 13:28 file_3_THREE.pdf
-rw-r--r--  1 kk  wheel    0 Jan 31 13:28 file_2_TWO.pdf
-rw-r--r--  1 kk  wheel    0 Jan 31 13:28 file_1_ONE.pdf
-rw-r--r--  1 kk  wheel  163 Jan 31 13:26 script.sh
This script lists the name of each file in the current folder in order of creation time along with an increasing counter. Change the echo line to do what you need :)
#!/bin/bash
((counter=1))
for f in $(ls -1ct); do
    echo $f-$counter
    ((counter+=1))
done
$(ls -1ct) is a bad habit. What if OP wants ONE instead of 1.
                
                somefile.pdf to somefile.pdf-44 (for an example value of 44).
                
                
ONEa place-holder? (If so, please edit your question to show what you really want.) Why does the second file get._TWOadded (with a.), but the first file gets only_ONE?