$check ="ABCD" # this value will come from an array 
        # ...
                $var = substr($file_name, 0, 3);
                # ...
                if($var eq $check){
[download]

I don't think the condition could ever be possibly satisfied. Also, I wouldn't use non-descriptive variable names like $var and $newvar.

Is this approach correct way

More or less so. But your requirements are slightly sloppy and in particular there's a discrepancy between the description of the task and what the code more or less does, but if I understand them correctly, then I'd do something along the lines of:

sub scandir {
    my $dir=shift;
    my $test=join '|', map quotemeta, @_;
    chdir $dir;
    for (glob '*') {
        next unless /^($test)(.*)/;
        my $new="$1D$2";
        print "`$_' => `$new'\n";
        if (-e $new) {
            warn "Warning: `$new' exists\n";
            # or do something more complex...
            next;
        } else {
            rename $_, $new or die "Can't rename to `$new': $!\n";
        }
    }
}
[download]

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