How about:

#!/usr/bin/perl

while(<DATA>) {
        chomp;
        if( /\A[\w]{3}_\w+_ear\Z/ ) {  
                print "$_ matches \n";
        }
        else {
                print "no joy for $_ \n";
        }
}

__DATA__
ab_wehave_noear
abc_test_ear
abc_test_two_ear
abcc_test_ear
[download]

which prints:

no joy for ab_wehave_noear
abc_test_ear matches
abc_test_two_ear matches
no joy for abcc_test_ear
[download]

I realize your problem definition said "characters" not "word thingies". I'm confident you can munge it to match your expected input range.