A couple of comments fist:

• Are you converting character encodings with your list of s/// statements? There are better ways of doing that if you are. On the other hand, if you already have some form of mangled data, this may be the best that can be done.
• Your formatting makes the block structure of your code unclear.
• You are processing what looks like CSV data by hand. Take a look at Text::CSV and other modules that already handle this type of data much better.

#!/usr/local/bin/perl -w
#
$fn1 = '/in.CSV';

# Useless stringification, and check your errors
# open (INST,"$fn1")
open(INST, '<', $fn1) or die "Unable to open '$fn1' for reading: $!";

# Preference, but possibly a better habit
# consider: open(ABI, ">$foo") where $foo
# contains ">blah".
# Also - check your errors
# open (ABI,">/out.ins");
open(ABI,">", "/out.ins") or die "Unable to open /out.ins: $!";

while (<INST>) { 
    # Moved from below - fail fast [1]
    next if /^"Branchno"\t/;
    next if /^""\t/;

    # Not necessary [3]
    # chomp;

    # Fishy - does this remove the last \t? [2]
    # chop;

    s/\õ/\ä/g;
    s/\"-/\"Ä/g;
    s/\--/\-Ä/g;
    s/\ - /\*-*/g;
    s/\ -/\ Ä/g;
    s/\*-*/\ - /g;
    s/\"_/\"Ü/g;
    s/\ _/\ Ü/g;
    s/\__/\_Ü/g;
    s/\³/\ü/g;
    s/\§/\õ/g;

    # @array = ' ';  # Not necessary, useless
    # no longer necessary [1,2]
    # @array = split(/\t/);

    # Moved to top of loop - fail fast [1]
    # if ($array[0] eq "\"Branchno\"") { next; }
    # if ($array[0] eq "\"\"" ) {next;}

    # No longer necessary, assuming chop above removed \t [2]
    # $result = join ("|",@array)."|"; 

    # Replace split / join with another s/// [2]
    s/\t/|/g;

    # Work on $_, no longer need $result
    # $result =~ s/\"//g;
    # print  ABI $result,"\n";
    s/"//g;

    # newline not necessary since chomp removed [3]
    print;

}
close (INST);
close (ABI);
[download]

1. If you fail fast, you can avoid doing the s/// on the discarded lines.
2. If "\t" was removed by the chop, this will handle it as well
3. If you don't chomp, you don't need to print the newline, as it is still there

There are also some tr/// uses that could possibly make this faster (see trizen's post above). However given the type of input data I am assuming from your code, this is a very fragile solution.