Your post is full of inconsistencies.

1. On the one hand you say "remove the spaces between the string not beginning or end of string"; which can be simply achieved thus:

   $s = ' input reset ; ';;
   $s =~ s[(?!^)(\s+)(?!$)][]g;;  ## replace all spaces -- that are neith
   +er preceded by the start of string; nor followed by the end-of-string
   + -- with nothing.
   print "'$s'";;
   ' inputreset; '
   [download]

2. But then you give this: reset. input reset ; how as a example,

   but with no delimiters, there's no way to know what the actual example you have in mind contains.

3. Additionally you say: "I want to remove the space only between reset and ; and not between input and reset"

   But the space between 'input' & 'reset' is neither at the beginning nor the end; but you say you don't want to remove it.

   Which completely contradicts your opening statement?

So, you need to explain your requirements far more clearly; with clearly delimited examples of inputs and required outputs; otherwise we're just guessing.

s/\S\K +(?=\S)//g
[download]

#!/usr/bin/perl --
use strict; 
use warnings;
use Data::Dump qw/ dd /;
my $msg = NoMiddleSpaces( ' i t s a r a c e ' );
dd( $msg );
sub NoMiddleSpaces {
    my( $start, $middle, $end ) = $_[0] =~ m{^(\s*)(.*?)(\s*$)}is;
    $middle =~ s{\s+}{}g;
    return "$start$middle$end";
}
__END__
" itsarace "
[download]