diff --git a/ipykernel/inprocess/ipkernel.py b/ipykernel/inprocess/ipkernel.py
index 13b17217a..cbbe85278 100644
--- a/ipykernel/inprocess/ipkernel.py
+++ b/ipykernel/inprocess/ipkernel.py
@@ -104,6 +104,7 @@ def _input_request(self, prompt, ident, parent, password=False):
         assert self.session is not None
         msg = self.session.msg("input_request", content, parent)
         for frontend in self.frontends:
+            assert frontend is not None
             if frontend.session.session == parent["header"]["session"]:
                 frontend.stdin_channel.call_handlers(msg)
                 break
@@ -138,6 +139,7 @@ def _io_dispatch(self, change):
         assert self.session is not None
         ident, msg = self.session.recv(self.iopub_socket.io_thread.socket, copy=False)
         for frontend in self.frontends:
+            assert frontend is not None
             frontend.iopub_channel.call_handlers(msg)
 
     # ------ Trait initializers -----------------------------------------------
diff --git a/ipykernel/kernelapp.py b/ipykernel/kernelapp.py
index de4682f86..af9629015 100644
--- a/ipykernel/kernelapp.py
+++ b/ipykernel/kernelapp.py
@@ -443,7 +443,7 @@ def log_connection_info(self):
             self.log.info(line)
         # also raw print to the terminal if no parent_handle (`ipython kernel`)
         # unless log-level is CRITICAL (--quiet)
-        if not self.parent_handle and int(self.log_level) < logging.CRITICAL:
+        if not self.parent_handle and int(self.log_level) < logging.CRITICAL:  # type:ignore[call-overload]
             print(_ctrl_c_message, file=sys.__stdout__)
             for line in lines:
                 print(line, file=sys.__stdout__)
@@ -700,7 +700,7 @@ def initialize(self, argv=None):
         except Exception:
             # Catch exception when initializing signal fails, eg when running the
             # kernel on a separate thread
-            if int(self.log_level) < logging.CRITICAL:
+            if int(self.log_level) < logging.CRITICAL:  # type:ignore[call-overload]
                 self.log.error("Unable to initialize signal:", exc_info=True)
         self.init_kernel()
         # shell init steps
diff --git a/ipykernel/kernelbase.py b/ipykernel/kernelbase.py
index 6d06d4ab5..8f3c0a50a 100644
--- a/ipykernel/kernelbase.py
+++ b/ipykernel/kernelbase.py
@@ -2,6 +2,7 @@
 
 # Copyright (c) IPython Development Team.
 # Distributed under the terms of the Modified BSD License.
+from __future__ import annotations
 
 import asyncio
 import concurrent.futures
@@ -80,7 +81,7 @@ class Kernel(SingletonConfigurable):
     # attribute to override with a GUI
     eventloop = Any(None)
 
-    processes: t.Dict[str, psutil.Process] = {}
+    processes: dict[str, psutil.Process] = {}
 
     @observe("eventloop")
     def _update_eventloop(self, change):
@@ -93,7 +94,7 @@ def _update_eventloop(self, change):
     profile_dir = Instance("IPython.core.profiledir.ProfileDir", allow_none=True)
     shell_stream = Instance(ZMQStream, allow_none=True)
 
-    shell_streams = List(
+    shell_streams: List[t.Any] = List(
         help="""Deprecated shell_streams alias. Use shell_stream
 
         .. versionchanged:: 6.0
@@ -153,10 +154,10 @@ def _default_ident(self):
 
     # This should be overridden by wrapper kernels that implement any real
     # language.
-    language_info: t.Dict[str, object] = {}
+    language_info: dict[str, object] = {}
 
     # any links that should go in the help menu
-    help_links = List()
+    help_links: List[dict[str, str]] = List()
 
     # Experimental option to break in non-user code.
     # The ipykernel source is in the call stack, so the user
@@ -180,7 +181,7 @@ def _default_ident(self):
 
     # track associations with current request
     _allow_stdin = Bool(False)
-    _parents = Dict({"shell": {}, "control": {}})
+    _parents: Dict[str, t.Any] = Dict({"shell": {}, "control": {}})
     _parent_ident = Dict({"shell": b"", "control": b""})
 
     @property
@@ -291,7 +292,7 @@ async def poll_control_queue(self):
 
     async def _flush_control_queue(self):
         """Flush the control queue, wait for processing of any pending messages"""
-        tracer_future: t.Union[concurrent.futures.Future[object], asyncio.Future[object]]
+        tracer_future: concurrent.futures.Future[object] | asyncio.Future[object]
         if self.control_thread:
             control_loop = self.control_thread.io_loop
             # concurrent.futures.Futures are threadsafe
@@ -945,7 +946,7 @@ async def interrupt_request(self, stream, ident, parent):
         """Handle an interrupt request."""
         if not self.session:
             return
-        content: t.Dict[str, t.Any] = {"status": "ok"}
+        content: dict[str, t.Any] = {"status": "ok"}
         try:
             self._send_interrupt_children()
         except OSError as err:
diff --git a/pyproject.toml b/pyproject.toml
index 1868b40b3..c06ebb18c 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -112,7 +112,7 @@ matrix.qt.features = [
 
 [tool.hatch.envs.typing]
 features = ["test"]
-dependencies = ["mypy>=1.6.0", "traitlets>=5.12.0", "ipython>=8.16.1", "jupyter_client>=8.5"]
+dependencies = ["mypy>=1.6.0", "traitlets>=5.13.0", "ipython>=8.16.1", "jupyter_client>=8.5"]
 [tool.hatch.envs.typing.scripts]
 test = "mypy --install-types --non-interactive {args}"