diff --git a/qiskit_experiments/library/randomized_benchmarking/interleaved_rb_experiment.py b/qiskit_experiments/library/randomized_benchmarking/interleaved_rb_experiment.py
index cf3c40d7a8..5b593254da 100644
--- a/qiskit_experiments/library/randomized_benchmarking/interleaved_rb_experiment.py
+++ b/qiskit_experiments/library/randomized_benchmarking/interleaved_rb_experiment.py
@@ -19,6 +19,7 @@
 from qiskit import QuantumCircuit
 from qiskit.circuit import Instruction
 from qiskit.quantum_info import Clifford
+from qiskit.exceptions import QiskitError
 
 from .rb_experiment import StandardRB
 from .interleaved_rb_analysis import InterleavedRBAnalysis
@@ -71,7 +72,7 @@ def __init__(
                            sequences are constructed by appending additional
                            Clifford samples to shorter sequences.
         """
-        self._interleaved_element = interleaved_element
+        self._set_interleaved_element(interleaved_element)
         super().__init__(qubits, lengths, num_samples, seed, full_sampling)
 
     def _sample_circuits(self, lengths, seed=None):
@@ -107,3 +108,23 @@ def _interleave(self, element_list: List) -> List:
             new_element_list.append(element)
             new_element_list.append(self._interleaved_element)
         return new_element_list
+
+    def _set_interleaved_element(self, interleaved_element):
+        """Handle the various types of the interleaved element
+
+        Args:
+            interleaved_element: The element to interleave
+
+        Raises:
+            QiskitError: if there is no known conversion of interleaved_element
+            to a Clifford group element
+        """
+        try:
+            interleaved_element_op = Clifford(interleaved_element)
+            self._interleaved_element = (interleaved_element, interleaved_element_op)
+        except QiskitError as error:
+            raise QiskitError(
+                "Interleaved element {} could not be converted to Clifford element".format(
+                    interleaved_element.name
+                )
+            ) from error
diff --git a/qiskit_experiments/library/randomized_benchmarking/rb_experiment.py b/qiskit_experiments/library/randomized_benchmarking/rb_experiment.py
index bf9f3b29e1..d917dd47fd 100644
--- a/qiskit_experiments/library/randomized_benchmarking/rb_experiment.py
+++ b/qiskit_experiments/library/randomized_benchmarking/rb_experiment.py
@@ -188,10 +188,16 @@ def _generate_circuit(
         circ_op = Clifford(np.eye(2 * self.num_qubits))
 
         for current_length, group_elt_circ in enumerate(elements):
-            group_elt_gate = group_elt_circ
+            if isinstance(group_elt_circ, tuple):
+                group_elt_gate = group_elt_circ[0]
+                group_elt_op = group_elt_circ[1]
+            else:
+                group_elt_gate = group_elt_circ
+                group_elt_op = Clifford(group_elt_circ)
+
             if not isinstance(group_elt_gate, Gate):
                 group_elt_gate = group_elt_gate.to_gate()
-            circ_op = circ_op.compose(Clifford(group_elt_circ))
+            circ_op = circ_op.compose(group_elt_op)
             for circ in circs:
                 circ.append(group_elt_gate, qubits)
                 circ.barrier(qubits)
diff --git a/test/randomized_benchmarking/test_rb.py b/test/randomized_benchmarking/test_rb.py
index 3a9fa3d532..af593d2bc4 100644
--- a/test/randomized_benchmarking/test_rb.py
+++ b/test/randomized_benchmarking/test_rb.py
@@ -26,6 +26,7 @@
 from qiskit.circuit.library import (
     XGate,
     CXGate,
+    TGate,
 )
 from qiskit_experiments.library import StandardRB, InterleavedRB
 
@@ -232,3 +233,16 @@ def test_interleaved_structure(self, interleaved_element: "Gate", qubits: list,
             self.assertEqual(c_int[int_idx + 3][0].name, interleaved_element.name)
             std_idx += 2
             int_idx += 4
+
+    def test_non_clifford_interleaved_element(self):
+        """Verifies trying to run interleaved RB with non Clifford element throws an exception"""
+        qubits = 1
+        lengths = [1, 4, 6, 9, 13, 16]
+        interleaved_element = TGate()  # T gate is not Clifford, this should fail
+        self.assertRaises(
+            QiskitError,
+            InterleavedRB,
+            interleaved_element,
+            qubits,
+            lengths,
+        )