You don't show us the code you have already written. This makes it hard for us to suggest you ways to improve your code.

You could use the following code, but it's likely even less efficient than a loop:

my $string = "\t\t\tfoo\t\tbar";

$string =~ s/^(\t+).*/$1/;
$string =~ s/\t/+1/g;
print eval $string, " tabs";
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By definition, it's impossible to repeat an action (check if the next character is a tab) an arbitrary number of times without using a loop.

Of course, nothing's stopping you from using existing loops.

my $num_leading_tabs = length( (/^(\t*)/)[0] );
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$string =~ /^(\t*)/;
$number_of_initial_tabs=length($1);
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tr as an alternative to length.

$ perl -E '
> $str = qq{\t\t\tcol1\tcol2};
> $str =~ m{^(\t+)};
> $leadingTabs = $1 =~ tr{\t}{};
> say $leadingTabs;'
3
$
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The length-based approaches are probably a bit faster, but this also seems to work:

>perl -wMstrict -le
"my $s = qq{\t\t\tX\t\t};
 my $n =()= $s =~ m{ \G \t }xmsg;
 print $n;
"
3
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Update: Removed pointless capture group from regex.