diff --git a/core/src/main/scala/cats/ApplicativeError.scala b/core/src/main/scala/cats/ApplicativeError.scala
index 4c21e72858..e52ef73578 100644
--- a/core/src/main/scala/cats/ApplicativeError.scala
+++ b/core/src/main/scala/cats/ApplicativeError.scala
@@ -104,6 +104,27 @@ trait ApplicativeError[F[_], E] extends Applicative[F] {
    */
   def handleError[A](fa: F[A])(f: E => A): F[A] = handleErrorWith(fa)(f.andThen(pure))
 
+  /**
+   * Void any error, by mapping it to `Unit`.
+   *
+   * This is useful when errors are reported via a side-channel but not directly handled.
+   * For example in Cats Effect:
+   *
+   * {{{
+   * IO.deferred[OutcomeIO[A]].flatMap { oc =>
+   *   ioa.guaranteeCase(oc.complete(_).void).void.voidError.start
+   *   // ...
+   * }
+   * }}}
+   *
+   * Without the `.voidError`, the Cats Effect runtime would consider an error in `ioa` to be
+   * unhandled and elevate it to [[scala.concurrent.ExecutionContext.reportFailure ExecutionContext#reportFailure]].
+   *
+   * @see [[handleError]] to map to an `A` value instead of `Unit`.
+   * @see [[https://github.com/typelevel/cats-effect/issues/3152 cats-effect#3152]]
+   */
+  def voidError(fu: F[Unit]): F[Unit] = handleError(fu)(Function.const(()))
+
   /**
    * Handle errors by turning them into [[scala.util.Either]] values.
    *
diff --git a/core/src/main/scala/cats/syntax/applicativeError.scala b/core/src/main/scala/cats/syntax/applicativeError.scala
index ff12673bb6..402c9f719a 100644
--- a/core/src/main/scala/cats/syntax/applicativeError.scala
+++ b/core/src/main/scala/cats/syntax/applicativeError.scala
@@ -34,6 +34,11 @@ trait ApplicativeErrorSyntax {
     fa: F[A]
   )(implicit F: ApplicativeError[F, E]): ApplicativeErrorOps[F, E, A] =
     new ApplicativeErrorOps[F, E, A](fa)
+
+  implicit final def catsSyntaxApplicativeErrorFUnit[F[_], E](
+    fu: F[Unit]
+  ): ApplicativeErrorFUnitOps[F, E] =
+    new ApplicativeErrorFUnitOps[F, E](fu)
 }
 
 /**
@@ -143,3 +148,8 @@ final class ApplicativeErrorOps[F[_], E, A](private val fa: F[A]) extends AnyVal
   def orRaise(other: => E)(implicit F: ApplicativeError[F, E]): F[A] =
     adaptErr { case _ => other }
 }
+
+final class ApplicativeErrorFUnitOps[F[_], E](private val fu: F[Unit]) extends AnyVal {
+  def voidError(implicit F: ApplicativeError[F, E]): F[Unit] =
+    F.voidError(fu)
+}
diff --git a/laws/src/main/scala/cats/laws/ApplicativeErrorLaws.scala b/laws/src/main/scala/cats/laws/ApplicativeErrorLaws.scala
index c6b21eeef3..180dccaaec 100644
--- a/laws/src/main/scala/cats/laws/ApplicativeErrorLaws.scala
+++ b/laws/src/main/scala/cats/laws/ApplicativeErrorLaws.scala
@@ -61,6 +61,9 @@ trait ApplicativeErrorLaws[F[_], E] extends ApplicativeLaws[F] {
   def attemptFromEitherConsistentWithPure[A](eab: Either[E, A]): IsEq[F[Either[E, A]]] =
     F.attempt(F.fromEither(eab)) <-> F.pure(eab)
 
+  def voidErrorConsistentWithHandleError(fu: F[Unit]): IsEq[F[Unit]] =
+    F.voidError(fu) <-> F.handleError(fu)(Function.const(()))
+
   def onErrorPure[A](a: A, f: E => F[Unit]): IsEq[F[A]] =
     F.onError(F.pure(a)) { case x => f(x) } <-> F.pure(a)
 
diff --git a/laws/src/main/scala/cats/laws/discipline/ApplicativeErrorTests.scala b/laws/src/main/scala/cats/laws/discipline/ApplicativeErrorTests.scala
index 6d0c4fd903..5597fad20a 100644
--- a/laws/src/main/scala/cats/laws/discipline/ApplicativeErrorTests.scala
+++ b/laws/src/main/scala/cats/laws/discipline/ApplicativeErrorTests.scala
@@ -75,6 +75,11 @@ trait ApplicativeErrorTests[F[_], E] extends ApplicativeTests[F] {
           "applicativeError attempt fromEither consistent with pure" -> forAll(
             laws.attemptFromEitherConsistentWithPure[A] _
           ),
+          "applicativeError voidError consistent with void+handleError" -> forAll { (a: A) =>
+            // Should be an implicit parameter but that is not a binary-compatible change
+            implicit val eqFUnit: Eq[F[Unit]] = makeEqFUnit[A](a)
+            forAll(laws.voidErrorConsistentWithHandleError _)
+          },
           "applicativeError onError pure" -> forAll(laws.onErrorPure[A] _),
           "applicativeError onError raise" -> forAll(laws.onErrorRaise[A] _),
           "applicativeError adaptError pure" -> forAll(laws.adaptErrorPure[A] _),
diff --git a/laws/src/main/scala/cats/laws/discipline/ApplicativeTests.scala b/laws/src/main/scala/cats/laws/discipline/ApplicativeTests.scala
index fc6ebbbe7a..8ac2829ee2 100644
--- a/laws/src/main/scala/cats/laws/discipline/ApplicativeTests.scala
+++ b/laws/src/main/scala/cats/laws/discipline/ApplicativeTests.scala
@@ -30,7 +30,7 @@ import org.scalacheck.{Arbitrary, Cogen, Gen}
 trait ApplicativeTests[F[_]] extends ApplyTests[F] {
   def laws: ApplicativeLaws[F]
 
-  private def makeEqFUnit[A](a: A)(implicit EqFA: Eq[F[A]]): Eq[F[Unit]] =
+  private[discipline] def makeEqFUnit[A](a: A)(implicit EqFA: Eq[F[A]]): Eq[F[Unit]] =
     Eq.by(fa => laws.F.as(fa, a))
 
   def applicative[A: Arbitrary, B: Arbitrary, C: Arbitrary](implicit
diff --git a/tests/shared/src/test/scala/cats/tests/SyntaxSuite.scala b/tests/shared/src/test/scala/cats/tests/SyntaxSuite.scala
index 829577afd5..79abb123d9 100644
--- a/tests/shared/src/test/scala/cats/tests/SyntaxSuite.scala
+++ b/tests/shared/src/test/scala/cats/tests/SyntaxSuite.scala
@@ -474,6 +474,9 @@ object SyntaxSuite {
     val ea = mock[E => A]
     val gea1 = ga.handleError(ea)
 
+    val geu = mock[G[Unit]]
+    val veu = geu.voidError
+
     val egea = mock[E => G[A]]
     val gea2 = ga.handleErrorWith(egea)