diff --git a/redis/commands/core.py b/redis/commands/core.py
index 525b31c99d..3b82699129 100644
--- a/redis/commands/core.py
+++ b/redis/commands/core.py
@@ -56,7 +56,9 @@
 
 if TYPE_CHECKING:
     import redis.asyncio.client
+    import redis.asyncio.cluster
     import redis.client
+    import redis.cluster
 
 
 class ACLCommands(CommandsProtocol):
@@ -5914,7 +5916,11 @@ class Script:
     An executable Lua script object returned by ``register_script``
     """
 
-    def __init__(self, registered_client: "redis.client.Redis", script: ScriptTextT):
+    def __init__(
+        self,
+        registered_client: Union["redis.client.Redis", "redis.cluster.RedisCluster"],
+        script: ScriptTextT,
+    ):
         self.registered_client = registered_client
         self.script = script
         # Precalculate and store the SHA1 hex digest of the script.
@@ -5930,7 +5936,7 @@ def __call__(
         self,
         keys: Union[Sequence[KeyT], None] = None,
         args: Union[Iterable[EncodableT], None] = None,
-        client: Union["redis.client.Redis", None] = None,
+        client: Union["redis.client.Redis", "redis.cluster.RedisCluster", None] = None,
     ):
         """Execute the script, passing any required ``args``"""
         keys = keys or []
@@ -5979,7 +5985,9 @@ class AsyncScript:
 
     def __init__(
         self,
-        registered_client: "redis.asyncio.client.Redis",
+        registered_client: Union[
+            "redis.asyncio.client.Redis", "redis.asyncio.cluster.RedisCluster"
+        ],
         script: ScriptTextT,
     ):
         self.registered_client = registered_client
@@ -6001,7 +6009,9 @@ async def __call__(
         self,
         keys: Union[Sequence[KeyT], None] = None,
         args: Union[Iterable[EncodableT], None] = None,
-        client: Union["redis.asyncio.client.Redis", None] = None,
+        client: Union[
+            "redis.asyncio.client.Redis", "redis.asyncio.cluster.RedisCluster", None
+        ] = None,
     ):
         """Execute the script, passing any required ``args``"""
         keys = keys or []
@@ -6234,7 +6244,10 @@ def script_load(self, script: ScriptTextT) -> ResponseT:
         """
         return self.execute_command("SCRIPT LOAD", script)
 
-    def register_script(self: "redis.client.Redis", script: ScriptTextT) -> Script:
+    def register_script(
+        self: Union["redis.client.Redis", "redis.cluster.RedisCluster"],
+        script: ScriptTextT,
+    ) -> Script:
         """
         Register a Lua ``script`` specifying the ``keys`` it will touch.
         Returns a Script object that is callable and hides the complexity of
@@ -6249,7 +6262,7 @@ async def script_debug(self, *args) -> None:
         return super().script_debug()
 
     def register_script(
-        self: "redis.asyncio.client.Redis",
+        self: Union["redis.asyncio.client.Redis", "redis.asyncio.cluster.RedisCluster"],
         script: ScriptTextT,
     ) -> AsyncScript:
         """
diff --git a/tests/test_asyncio/test_scripting.py b/tests/test_asyncio/test_scripting.py
index b8e100c04a..76592e7a93 100644
--- a/tests/test_asyncio/test_scripting.py
+++ b/tests/test_asyncio/test_scripting.py
@@ -1,6 +1,7 @@
 import pytest
 import pytest_asyncio
 from redis import exceptions
+from redis.commands.core import AsyncScript
 from tests.conftest import skip_if_server_version_lt
 
 multiply_script = """
@@ -150,3 +151,27 @@ async def test_eval_msgpack_pipeline_error_in_lua(self, r):
         with pytest.raises(exceptions.ResponseError) as excinfo:
             await pipe.execute()
         assert excinfo.type == exceptions.ResponseError
+
+
+@pytest.mark.onlycluster
+class TestAsyncScriptWithCluster:
+    """Tests for AsyncScript with RedisCluster support."""
+
+    @pytest_asyncio.fixture
+    async def r(self, create_redis):
+        redis = await create_redis()
+        yield redis
+        await redis.script_flush()
+
+    @pytest.mark.asyncio()
+    async def test_register_script_with_cluster_client(self, r):
+        """Test that register_script works with async RedisCluster client.
+
+        This verifies the type hints fix for register_script to support RedisCluster.
+        """
+        await r.set("a", 2)
+        multiply = r.register_script(multiply_script)
+        assert isinstance(multiply, AsyncScript)
+        assert multiply.registered_client is r
+        # Verify the script actually works
+        assert await multiply(keys=["a"], args=[3]) == 6
diff --git a/tests/test_scripting.py b/tests/test_scripting.py
index 899dc69482..9587285c0c 100644
--- a/tests/test_scripting.py
+++ b/tests/test_scripting.py
@@ -96,6 +96,19 @@ def test_eval_same_slot(self, r):
         result = r.eval(script, 2, "A{foo}", "B{foo}")
         assert result == 8
 
+    @pytest.mark.onlycluster
+    def test_register_script_with_cluster_client(self, r):
+        """Test that register_script works with RedisCluster client.
+
+        This verifies the type hints fix for register_script to support RedisCluster.
+        """
+        r.set("a", 2)
+        multiply = r.register_script(multiply_script)
+        assert isinstance(multiply, Script)
+        assert multiply.registered_client is r
+        # Verify the script actually works
+        assert multiply(keys=["a"], args=[3]) == 6
+
     @pytest.mark.onlycluster
     def test_eval_crossslot(self, r):
         """