diff --git a/qiskit/circuit/__init__.py b/qiskit/circuit/__init__.py
index 0608765a1248..af306bb32b93 100644
--- a/qiskit/circuit/__init__.py
+++ b/qiskit/circuit/__init__.py
@@ -220,6 +220,7 @@
 from .controlledgate import ControlledGate
 from .instruction import Instruction
 from .instructionset import InstructionSet
+from .circuit_element import CircuitElement
 from .barrier import Barrier
 from .delay import Delay
 from .measure import Measure
diff --git a/qiskit/circuit/instructionset.py b/qiskit/circuit/instructionset.py
index 263800ddc7e2..bdec5450375a 100644
--- a/qiskit/circuit/instructionset.py
+++ b/qiskit/circuit/instructionset.py
@@ -16,6 +16,7 @@
 from qiskit.circuit.exceptions import CircuitError
 from .instruction import Instruction
 from .classicalregister import Clbit
+from .circuit_element import CircuitElement
 
 
 class InstructionSet:
@@ -46,7 +47,7 @@ def __getitem__(self, i):
 
     def add(self, gate, qargs, cargs):
         """Add an instruction and its context (where it is attached)."""
-        if not isinstance(gate, Instruction):
+        if not isinstance(gate, CircuitElement):
             raise CircuitError("attempt to add non-Instruction" + " to InstructionSet")
         self.instructions.append(gate)
         self.qargs.append(qargs)
diff --git a/qiskit/circuit/quantumcircuit.py b/qiskit/circuit/quantumcircuit.py
index 2ca6e5ead696..a67d9ae1a2bb 100644
--- a/qiskit/circuit/quantumcircuit.py
+++ b/qiskit/circuit/quantumcircuit.py
@@ -56,6 +56,7 @@
 from .delay import Delay
 from .measure import Measure
 from .reset import Reset
+from .circuit_element import CircuitElement
 
 try:
     import pygments
@@ -1124,7 +1125,7 @@ def cbit_argument_conversion(self, clbit_representation: ClbitSpecifier) -> List
 
     def append(
         self,
-        instruction: Instruction,
+        instruction: CircuitElement,
         qargs: Optional[Sequence[QubitSpecifier]] = None,
         cargs: Optional[Sequence[ClbitSpecifier]] = None,
     ) -> InstructionSet:
@@ -1144,7 +1145,7 @@ def append(
             CircuitError: if object passed is neither subclass nor an instance of Instruction
         """
         # Convert input to instruction
-        if not isinstance(instruction, Instruction) and not hasattr(instruction, "to_instruction"):
+        if not isinstance(instruction, CircuitElement) and not hasattr(instruction, "to_instruction"):
             if issubclass(instruction, Instruction):
                 raise CircuitError(
                     "Object is a subclass of Instruction, please add () to "
@@ -1154,7 +1155,7 @@ def append(
             raise CircuitError(
                 "Object to append must be an Instruction or have a to_instruction() method."
             )
-        if not isinstance(instruction, Instruction) and hasattr(instruction, "to_instruction"):
+        if not isinstance(instruction, CircuitElement) and hasattr(instruction, "to_instruction"):
             instruction = instruction.to_instruction()
 
         # Make copy of parameterized gate instances
@@ -1172,7 +1173,7 @@ def append(
         return instructions
 
     def _append(
-        self, instruction: Instruction, qargs: Sequence[Qubit], cargs: Sequence[Clbit]
+        self, instruction: CircuitElement, qargs: Sequence[Qubit], cargs: Sequence[Clbit]
     ) -> Instruction:
         """Append an instruction to the end of the circuit, modifying
         the circuit in place.
@@ -1189,8 +1190,8 @@ def _append(
             CircuitError: if the gate is of a different shape than the wires
                 it is being attached to.
         """
-        if not isinstance(instruction, Instruction):
-            raise CircuitError("object is not an Instruction.")
+        if not isinstance(instruction, CircuitElement):
+            raise CircuitError("object is not a CircuitElement.")
 
         # do some compatibility checks
         self._check_dups(qargs)
diff --git a/qiskit/quantum_info/operators/symplectic/clifford.py b/qiskit/quantum_info/operators/symplectic/clifford.py
index 13dd35acec0d..809fd08c678e 100644
--- a/qiskit/quantum_info/operators/symplectic/clifford.py
+++ b/qiskit/quantum_info/operators/symplectic/clifford.py
@@ -16,7 +16,7 @@
 import numpy as np
 
 from qiskit.exceptions import QiskitError
-from qiskit.circuit import QuantumCircuit, Instruction
+from qiskit.circuit import QuantumCircuit, Instruction, CircuitElement
 from qiskit.circuit.library.standard_gates import IGate, XGate, YGate, ZGate, HGate, SGate
 from qiskit.quantum_info.operators.base_operator import BaseOperator
 from qiskit.quantum_info.operators.operator import Operator
@@ -27,7 +27,7 @@
 from .clifford_circuits import _append_circuit
 
 
-class Clifford(BaseOperator, AdjointMixin):
+class Clifford(BaseOperator, AdjointMixin, CircuitElement):
     """An N-qubit unitary operator from the Clifford group.
 
     **Representation**
@@ -525,6 +525,24 @@ def _pad_with_identity(self, clifford, qargs):
 
         return padded
 
+    # These implement the required methods of the CircuitElement mixin
+
+    @property
+    def name(self):
+        return 'clifford'
+
+    @property
+    def num_params(self):
+        return 1
+
+    @property
+    def num_clbits(self):
+        return  0
+
+    @property
+    def params(self):
+        return (self._table,)
+
 
 # Update docstrings for API docs
 generate_apidocs(Clifford)