diff --git a/.github/workflows/python-tests.yml b/.github/workflows/python-tests.yml
index 28fd018ce1..14eb1bca13 100644
--- a/.github/workflows/python-tests.yml
+++ b/.github/workflows/python-tests.yml
@@ -176,8 +176,11 @@ jobs:
     needs:
       - build
       - pre-commit
+      - test_docs
+      - test_minimum_versions
       - test_prereleases
-      - make_sdist
+      - client8
+      - check_links
       - test_sdist
     runs-on: ubuntu-latest
     steps:
diff --git a/pyproject.toml b/pyproject.toml
index 5a215f7de3..9a5ad677e0 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -30,7 +30,7 @@ dependencies = [
     "anyio>=3.1.0,<4",
     "argon2-cffi",
     "jinja2",
-    "jupyter_client>=7.2",
+    "jupyter_client>=7.4.4",
     "jupyter_core>=4.9.2",
     "jupyter_server_terminals",
     "nbconvert>=6.4.4",
@@ -38,10 +38,10 @@ dependencies = [
     "packaging",
     "prometheus_client",
     "pywinpty;os_name=='nt'",
-    "pyzmq>=17",
+    "pyzmq>=24",
     "Send2Trash",
     "terminado>=0.8.3",
-    "tornado>=6.1.0",
+    "tornado>=6.2.0",
     "traitlets>=5.1",
     "websocket-client",
     "jupyter_events>=0.4.0"