Maybe factor out the common $front in each return statement to make one return statement: 
sub insert_after_first {
    return if @_ < 3;
    my ( $elem, $new, $front ) = splice @_, 0, 3;
    return ( $front,
             $front eq $elem
             ? ($new, @_ )
             : insert_after_first( $elem, $new, @_ )
           );
}

[download]
Update: Oo! In fact, you don't do anything with $new, except stick it back on the front of @_, so don't take it off: 
sub insert_after_first {
    return if @_ < 3;
    my ( $elem, $front ) = (splice(@_, 0, 1), splice(@_, 1, 1));
    return ( $front,
             $front eq $elem
             ? @_
             : insert_after_first( $elem, @_ )
             );
}

[download]
Then, to change Lispish elegance to Perlish elegance (or madness), make your argument list the way you want it for the recursion, and use & without parentheses to recurse: 
sub insert_after_first {
    return if @_ < 3;
    my $front = splice(@_, 2, 1);
    return ( $front,
             $front eq $_[0]
             ? @_[1..$#_]
             : &insert_after_first
       );
}

[download]
Caution: Contents may have been coded under pressure.

In reply to Re^2: Inserting an element into an array after a certain element by Roy Johnson
in thread Inserting an element into an array after a certain element by saintmike

Title:
Use:  <p> text here (a paragraph) </p>
and:  <code> code here </code>
to format your post, it's "PerlMonks-approved HTML":


  • Posts are HTML formatted. Put <p> </p> tags around your paragraphs. Put <code> </code> tags around your code and data!
  • Titles consisting of a single word are discouraged, and in most cases are disallowed outright.
  • Read Where should I post X? if you're not absolutely sure you're posting in the right place.
  • Please read these before you post! —
  • Posts may use any of the Perl Monks Approved HTML tags:
    a, abbr, b, big, blockquote, br, caption, center, col, colgroup, dd, del, details, div, dl, dt, em, font, h1, h2, h3, h4, h5, h6, hr, i, ins, li, ol, p, pre, readmore, small, span, spoiler, strike, strong, sub, summary, sup, table, tbody, td, tfoot, th, thead, tr, tt, u, ul, wbr
  • You may need to use entities for some characters, as follows. (Exception: Within code tags, you can put the characters literally.)
            For:     Use:
    & &amp;
    < &lt;
    > &gt;
    [ &#91;
    ] &#93;
  • Link using PerlMonks shortcuts! What shortcuts can I use for linking?
  • See Writeup Formatting Tips and other pages linked from there for more info.