diff --git a/Changes.md b/Changes.md
index 3aa6dbc2f..e5b66acea 100644
--- a/Changes.md
+++ b/Changes.md
@@ -22,6 +22,8 @@ require "sidekiq/middleware/current_attributes"
 Sidekiq::CurrentAttributes.persist(Myapp::Current) # Your AS:CurrentAttributes singleton
 ```
 - Retry Redis operation if we get an `UNBLOCKED` Redis error. [#4985]
+- **BREAKING CHANGE** Run existing signal-handling code, if there is any, before running sidekiq's
+  signal-handling code. [#4991]
 
 6.2.2
 ---------
diff --git a/lib/sidekiq/cli.rb b/lib/sidekiq/cli.rb
index df6339a67..8398759df 100644
--- a/lib/sidekiq/cli.rb
+++ b/lib/sidekiq/cli.rb
@@ -46,7 +46,14 @@ def run(boot_app: true)
       # USR1 and USR2 don't work on the JVM
       sigs << "USR2" if Sidekiq.pro? && !jruby?
       sigs.each do |sig|
-        trap sig do
+        old_handler = Signal.trap(sig) do
+          if old_handler.respond_to?(:call)
+            begin
+              old_handler.call
+            rescue Exception
+              puts $!.inspect
+            end
+          end
           self_write.puts(sig)
         end
       rescue ArgumentError