use Data::Dumper;
%myhash = ( 1 => 'a', 2=> 'b', 3=> 'a', 4=>'c', 5 => 'a', 6 => 'a', 7 =>'b');
%newhash = map { ($_,$myhash{$_}) }  grep { $myhash{$_} eq 'a'; } keys %myhash ;
print Dumper \%newhash;