diff --git a/cosmos/operators/local.py b/cosmos/operators/local.py
index 69bc1a78c..adf608643 100644
--- a/cosmos/operators/local.py
+++ b/cosmos/operators/local.py
@@ -405,10 +405,21 @@ class DbtRunLocalOperator(DbtLocalBaseOperator):
     ui_color = "#7352BA"
     ui_fgcolor = "#F4F2FC"
 
-    def __init__(self, **kwargs: Any) -> None:
+    def __init__(self, full_refresh: bool = False, **kwargs: Any) -> None:
+        self.full_refresh = full_refresh
         super().__init__(**kwargs)
         self.base_cmd = ["run"]
 
+    def add_cmd_flags(self) -> list[str]:
+        flags = []
+        if self.full_refresh is True:
+            flags.append("--full-refresh")
+        return flags
+
+    def execute(self, context: Context) -> None:
+        cmd_flags = self.add_cmd_flags()
+        self.build_and_run_cmd(context=context, cmd_flags=cmd_flags)
+
 
 class DbtTestLocalOperator(DbtLocalBaseOperator):
     """
@@ -485,6 +496,10 @@ def add_cmd_flags(self) -> list[str]:
             flags.append(yaml.dump(self.args))
         return flags
 
+    def execute(self, context: Context) -> None:
+        cmd_flags = self.add_cmd_flags()
+        self.build_and_run_cmd(context=context, cmd_flags=cmd_flags)
+
 
 class DbtDocsLocalOperator(DbtLocalBaseOperator):
     """
diff --git a/tests/operators/test_local.py b/tests/operators/test_local.py
index 7d00d88c8..f926816f6 100644
--- a/tests/operators/test_local.py
+++ b/tests/operators/test_local.py
@@ -11,7 +11,18 @@
 from pendulum import datetime
 
 from cosmos.config import ProfileConfig
-from cosmos.operators.local import DbtLocalBaseOperator, DbtRunLocalOperator, DbtTestLocalOperator
+from cosmos.operators.local import (
+    DbtLocalBaseOperator,
+    DbtLSLocalOperator,
+    DbtSnapshotLocalOperator,
+    DbtRunLocalOperator,
+    DbtTestLocalOperator,
+    DbtDocsLocalOperator,
+    DbtDocsS3LocalOperator,
+    DbtDocsAzureStorageLocalOperator,
+    DbtSeedLocalOperator,
+    DbtRunOperationLocalOperator,
+)
 from cosmos.profiles import PostgresUserPasswordProfileMapping
 from tests.utils import test_dag as run_test_dag
 
@@ -228,3 +239,49 @@ def test_store_compiled_sql() -> None:
             tmp_project_dir="my/dir",
             context=Context(execution_date=datetime(2023, 2, 15, 12, 30)),
         )
+
+
+@pytest.mark.parametrize(
+    "operator_class,kwargs,expected_call_kwargs",
+    [
+        (DbtSeedLocalOperator, {"full_refresh": True}, {"context": {}, "cmd_flags": ["--full-refresh"]}),
+        (DbtRunLocalOperator, {"full_refresh": True}, {"context": {}, "cmd_flags": ["--full-refresh"]}),
+        (
+            DbtRunOperationLocalOperator,
+            {"args": {"days": 7, "dry_run": True}, "macro_name": "bla"},
+            {"context": {}, "cmd_flags": ["--args", "days: 7\ndry_run: true\n"]},
+        ),
+    ],
+)
+@patch("cosmos.operators.local.DbtLocalBaseOperator.build_and_run_cmd")
+def test_operator_execute_with_flags(mock_build_and_run_cmd, operator_class, kwargs, expected_call_kwargs):
+    task = operator_class(profile_config=profile_config, task_id="my-task", project_dir="my/dir", **kwargs)
+    task.execute(context={})
+    mock_build_and_run_cmd.assert_called_once_with(**expected_call_kwargs)
+
+
+@pytest.mark.parametrize(
+    "operator_class",
+    (
+        DbtLSLocalOperator,
+        DbtSnapshotLocalOperator,
+        DbtTestLocalOperator,
+        DbtDocsLocalOperator,
+        DbtDocsS3LocalOperator,
+        DbtDocsAzureStorageLocalOperator,
+    ),
+)
+@patch("cosmos.operators.local.DbtLocalBaseOperator.build_and_run_cmd")
+def test_operator_execute_without_flags(mock_build_and_run_cmd, operator_class):
+    operator_class_kwargs = {
+        DbtDocsS3LocalOperator: {"aws_conn_id": "fake-conn", "bucket_name": "fake-bucket"},
+        DbtDocsAzureStorageLocalOperator: {"azure_conn_id": "fake-conn", "container_name": "fake-container"},
+    }
+    task = operator_class(
+        profile_config=profile_config,
+        task_id="my-task",
+        project_dir="my/dir",
+        **operator_class_kwargs.get(operator_class, {}),
+    )
+    task.execute(context={})
+    mock_build_and_run_cmd.assert_called_once_with(context={})