OK, so it was an interesting problem:

use strict;
use warnings;
use DBI;

my $dbfile = 'D:\Delme~~\demo.db';

unlink $dbfile;

my $dbh = DBI->connect("dbi:SQLite:dbname=$dbfile","","");

$dbh->do (qq{CREATE TABLE Demo (rowid INTEGER, old VARCHAR(9), new VAR
+CHAR(3))});

my @testData = (
    ['ABFD-1234'  => 'AAA'],
    ['ABFD-178G'  => 'BBB'],
    ['F2HB-9401'  => 'AAA'],
    ['ZDDR-00W5' => 'DDD'],
    ['D7*D-48*6' => 'EEE'],
    ['*7RD-4896' => 'FFF'],
    ['D7RD-489*' => 'GGG'],
);
my @old = map {$_->[0]} @testData;
my @new = map {$_->[1]} @testData;
my $sth = $dbh->prepare (qq{INSERT INTO Demo (old, new) VALUES (?, ?)}
+);
my $entries = $sth->execute_array ({}, \@old, \@new);

$sth = $dbh->prepare (qq{SELECT old, new FROM Demo WHERE old LIKE ?});
$sth->execute ('%*%');

my @candidates = @{$sth->fetchall_arrayref ()};

for my $target ('D7PD', 'D7RD', '4897', '4876') {
    for my $candidate (map {$_->[0]} @candidates) {
        my @parts = split '\*', $candidate;
        my @rParts = reverse map {scalar reverse $_} @parts;
        my $str = $target;
        my $rStr = reverse $target;

        eval {
            matchPart($str, $_) || return for @parts;
            return !length $str;
            }
        or eval {
            $str = '';
            rMatchPart($rStr, $_) || return for @rParts;
            return ! length $rStr;
            }
        or next;

        print "Matched '$target' against '$candidate'\n" if !length $s
+tr;
    }
}


sub matchPart {
    my ($str, $match) = @_;

    $match = substr $match, 0, length $_[0];
    return 1 if $_[0] =~ s/$match.?//;
}


sub rMatchPart {
    my ($str, $match) = @_;

    $match = substr $match, 0, length($str) - 1 if length $str;
    return 1 if $_[0] =~ s/.?$match//;
}
[download]

Prints:

Matched 'D7PD' against 'D7*D-48*6'
Matched 'D7RD' against 'D7*D-48*6'
Matched 'D7RD' against '*7RD-4896'
Matched 'D7RD' against 'D7RD-489*'
Matched '4897' against 'D7RD-489*'
[download]

Only marginally tested. There are lots of edge cases that may be problematic, but maybe it's a hint in a useful direction.

Update: removed an edge case.