That subroutine has large amounts of cut&paste code that could be reduced, but mostly that wouldn't affect the performance.

Two changes that might improve it are:

1. Three occurrences of $HoH{$p} =  {%rec}; could become $HoH{$p} =  \%rec; without affecting the program, but avoiding replication of existing hashes.
2. One occurance of  push @data, {%HoH}; can become  push @data, \%HoH; for the same reason.

This is total speculation given the number of variables used within this sub but not declared there, so take it with a pinch of salt, but the subroutine may be reducable to something along the lines of:

sub main {
    my $csv = Text::CSV_XS->new;
    for( @files ) {
        open( NOW , "$directory/$_" ) || die "you suck\n";
        while( <NOW> ) {
            chomp;
            my( %rec, %HoH, $p );
            $t_counter++;

            my( $attrsRef, @selectedFields ) =
                /^STOP/     ? ( \@attrs_sto, 0,1,13,14,16,20,33,34,36,
+67 ) :
                /^START/    ? ( \@attrs_sta, 0,1,11,15,28,29,31,53    
+   ) :
                /^ATTEMPT/  ? ( \@attrs_att, 0,1,11,13,17,30,31,33,57 
+   ) :
                $ncounter++;
            ;

            my %rec{ @$attrs_ref ) = @fields{ @selectedFields );
            my $p =
                $rec{ _i_pstn_trunk } ? extract( $rec{ _i_pstn_circuit
+ }, $rec{ _i_pstn_trunk } ) :
                $rec{ _e_pstn_trunk } ? extract( $rec{ _e_pstn_circuit
+ }, $rec{ _e_pstn_trunk } ) :
                $ncounter++
            ;

            $csv->parse( $_ );
            my @fields = $csv->fields;

            push @data, \%HoH;
        }
        close NOW;
    }
}
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The main unknown is the significance of the variable $ncounter? (BTW: Naming a variable $somethingcounter is ... That it is a counter is obvious from it's usage, but one letter to signify what it is counting, when it is declared at a higher level, does not convey much information.

On similar lines, having arrays called @attrs_sto, @attrs_sta, and @attrs_att, presumably STOP, START and ATTEMPT, minimises the important information (to just one character sometimes) and maximises the less important common element.