diff --git a/changelog.d/17536.misc b/changelog.d/17536.misc
new file mode 100644
index 00000000000..116ef0c36d1
--- /dev/null
+++ b/changelog.d/17536.misc
@@ -0,0 +1 @@
+Replace override of deprecated method `HTTPAdapter.get_connection` with `get_connection_with_tls_context`.
\ No newline at end of file
diff --git a/scripts-dev/federation_client.py b/scripts-dev/federation_client.py
index 4c758e5424e..fb879ef5555 100755
--- a/scripts-dev/federation_client.py
+++ b/scripts-dev/federation_client.py
@@ -43,7 +43,7 @@
 import base64
 import json
 import sys
-from typing import Any, Dict, Optional, Tuple
+from typing import Any, Dict, Mapping, Optional, Tuple, Union
 from urllib import parse as urlparse
 
 import requests
@@ -75,7 +75,7 @@ def encode_canonical_json(value: object) -> bytes:
         value,
         # Encode code-points outside of ASCII as UTF-8 rather than \u escapes
         ensure_ascii=False,
-        # Remove unecessary white space.
+        # Remove unnecessary white space.
         separators=(",", ":"),
         # Sort the keys of dictionaries.
         sort_keys=True,
@@ -298,12 +298,23 @@ def send(
 
         return super().send(request, *args, **kwargs)
 
-    def get_connection(
-        self, url: str, proxies: Optional[Dict[str, str]] = None
+    def get_connection_with_tls_context(
+        self,
+        request: PreparedRequest,
+        verify: Optional[Union[bool, str]],
+        proxies: Optional[Mapping[str, str]] = None,
+        cert: Optional[Union[Tuple[str, str], str]] = None,
     ) -> HTTPConnectionPool:
-        # overrides the get_connection() method in the base class
-        parsed = urlparse.urlsplit(url)
-        (host, port, ssl_server_name) = self._lookup(parsed.netloc)
+        # overrides the get_connection_with_tls_context() method in the base class
+        parsed = urlparse.urlsplit(request.url)
+
+        # Extract the server name from the request URL, and ensure it's a str.
+        hostname = parsed.netloc
+        if isinstance(hostname, bytes):
+            hostname = hostname.decode("utf-8")
+        assert isinstance(hostname, str)
+
+        (host, port, ssl_server_name) = self._lookup(hostname)
         print(
             f"Connecting to {host}:{port} with SNI {ssl_server_name}", file=sys.stderr
         )