Deprecate execute()

qiskit/execute_function.py

@@ -275,6 +275,12 @@ def execute(
 
             job = execute(qc, backend, shots=4321)
     """
+    warnings.warn('The execute() function in Qiskit is deprecated as of Qiskit Terra 0.21.0, '
+                  'and will be removed in a future release. '
+                  'Instead, please use transpile() followed by backend.run(). '
+                  'Alternatively, to achieve a similar high-level functionality, please '
+                  'use qiskit primitives.',
+                  DeprecationWarning, stacklevel=2)
     if isinstance(experiments, (Schedule, ScheduleBlock)) or (
         isinstance(experiments, list) and isinstance(experiments[0], (Schedule, ScheduleBlock))
     ):

releasenotes/notes/deprecate-execute-67a5c68b93722057.yaml

@@ -0,0 +1,20 @@
+---
+deprecations:
+  - |
+    Qiskit's :func:`~.execute_function.execute` function is deprecated.
+    This function served as a high-level wrapper around transpiling
+    a circuit with some transpile options and running it on a backend
+    with some run options. To do the same thing, you can explicitly
+    use the :func:`~.transpile` function (with appropriate transpile
+    options) followed by `backend.run()` (with appropriate run options).
+
+   For example, instead of running::
+
+      from qiskit import execute
+      job = execute(circuit, backend)
+
+   you can run::
+
+      from qiskit import transpile
+      new_circuit = transpile(circuit)
+      job = backend.run(new_circuit)