Corion's approach is the correct one. However, since you asked using a regex on the string and have still not shown that you have learned How to ask better questions using Test::More and sample data, here is one final demonstration.

use strict;
use warnings;

use Test::More tests => 1;

my $response1 = <<EOT;
Cache-Control: no-cache, no-store
Connection: close
Date: Fri, 26 Mar 2021 02:11:16 GMT
Pragma: no-cache
Server: nginx
Vary: Accept-Encoding
Content-Type: application/json
Expires: 0
Client-Date: Fri, 26 Mar 2021 02:11:16 GMT
Client-Peer: 10.10.1.32:8080
Client-Response-Num: 1
Client-Transfer-Encoding: chunked
Expect-Ct: report-uri="https://org.extract.net", max-age=0
Link: <https://sso.myorg.com/api/v5/myids?limit=200>; rel="self"
Link: <https://sso.myorg.com/api/v5/myids?after=200xxxxxxxxxxxxxxxxx&l
+imit=200>; rel="next"
EOT

my $want = '<https://sso.myorg.com/api/v5/myids?after=200xxxxxxxxxxxxx
+xxxx&limit=200>; rel="next"';

my @linkheader = $response1 =~ /^Link: (.*"next")/mg;
is $linkheader[0], $want;
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