diff --git a/pyproject.toml b/pyproject.toml
index 74cc3650e..f7e7e5bcb 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -121,11 +121,11 @@ packages = ["/cosmos"]
 [tool.hatch.envs.tests]
 dependencies = [
     "astronomer-cosmos[tests]",
-    "apache-airflow-providers-postgres==5.11.0",
     "apache-airflow-providers-cncf-kubernetes>=5.1.1",
     "apache-airflow-providers-amazon>=3.0.0,<8.20.0", # https://github.com/apache/airflow/issues/39103
     "apache-airflow-providers-docker>=3.5.0",
     "apache-airflow-providers-microsoft-azure",
+    "apache-airflow-providers-postgres",
     "types-PyYAML",
     "types-attrs",
     "types-requests",
diff --git a/tests/operators/test_local.py b/tests/operators/test_local.py
index 0f35705b6..14ed66027 100644
--- a/tests/operators/test_local.py
+++ b/tests/operators/test_local.py
@@ -23,7 +23,6 @@
     parse_number_of_warnings_dbt_runner,
     parse_number_of_warnings_subprocess,
 )
-from cosmos.exceptions import AirflowCompatibilityError
 from cosmos.operators.local import (
     DbtBuildLocalOperator,
     DbtDocsAzureStorageLocalOperator,
@@ -443,48 +442,6 @@ def test_run_operator_dataset_inlets_and_outlets(caplog):
     assert test_operator.outlets == []
 
 
-@pytest.mark.skipif(
-    version.parse(airflow_version) not in PARTIALLY_SUPPORTED_AIRFLOW_VERSIONS,
-    reason="Airflow 2.9.0 and 2.9.1 have a breaking change in Dataset URIs",
-    # https://github.com/apache/airflow/issues/39486
-)
-@pytest.mark.integration
-def test_run_operator_dataset_emission_fails(caplog):
-
-    with DAG("test-id-1", start_date=datetime(2022, 1, 1)) as dag:
-        seed_operator = DbtSeedLocalOperator(
-            profile_config=real_profile_config,
-            project_dir=DBT_PROJ_DIR,
-            task_id="seed",
-            dbt_cmd_flags=["--select", "raw_customers"],
-            install_deps=True,
-            append_env=True,
-        )
-        run_operator = DbtRunLocalOperator(
-            profile_config=real_profile_config,
-            project_dir=DBT_PROJ_DIR,
-            task_id="run",
-            dbt_cmd_flags=["--models", "stg_customers"],
-            install_deps=True,
-            append_env=True,
-        )
-
-        seed_operator >> run_operator
-
-    with pytest.raises(AirflowCompatibilityError) as exc:
-        run_test_dag(dag)
-
-    err_msg = str(exc.value)
-    assert (
-        "Apache Airflow 2.9.0 & 2.9.1 introduced a breaking change in Dataset URIs, to be fixed in newer versions"
-        in err_msg
-    )
-    assert (
-        "If you want to use Cosmos with one of these Airflow versions, you will have to disable emission of Datasets"
-        in err_msg
-    )
-
-
 @pytest.mark.skipif(
     version.parse(airflow_version) not in PARTIALLY_SUPPORTED_AIRFLOW_VERSIONS,
     reason="Airflow 2.9.0 and 2.9.1 have a breaking change in Dataset URIs",