diff --git a/CHANGES.md b/CHANGES.md
index 2249f62d625..d93c5b8ed96 100644
--- a/CHANGES.md
+++ b/CHANGES.md
@@ -39,6 +39,9 @@ Second Release Candidate for Cylc 8 suitable for acceptance testing.
 validating/running a Jinja2 workflow (for users who have installed Cylc
 using `pip`.)
 
+[#4737](https://github.com/cylc/cylc-flow/pull/4737) -
+Fix issue which prevented tasks with incomplete outputs from being rerun by
+subsequent flows.
 
 -------------------------------------------------------------------------------
 ## __cylc-8.0rc1 (<span actions:bind='release-date'>Released 2022-02-17</span>)__
diff --git a/cylc/flow/flow_mgr.py b/cylc/flow/flow_mgr.py
index 12c0e6423f8..3dc0d997760 100644
--- a/cylc/flow/flow_mgr.py
+++ b/cylc/flow/flow_mgr.py
@@ -23,6 +23,9 @@
 from cylc.flow.workflow_db_mgr import WorkflowDatabaseManager
 
 
+FlowNums = Set[int]
+
+
 class FlowMgr:
     """Logic to manage flow counter and flow metadata."""
 
@@ -55,7 +58,7 @@ def get_new_flow(self, description: Optional[str] = None) -> int:
         )
         return self.counter
 
-    def load_from_db(self, flow_nums: Set[int]) -> None:
+    def load_from_db(self, flow_nums: FlowNums) -> None:
         """Load flow data for scheduler restart.
 
         Sets the flow counter to the max flow number in the DB.
diff --git a/cylc/flow/task_pool.py b/cylc/flow/task_pool.py
index 2a1cd690f53..ce4b2f38724 100644
--- a/cylc/flow/task_pool.py
+++ b/cylc/flow/task_pool.py
@@ -68,7 +68,7 @@
     from cylc.flow.taskdef import TaskDef
     from cylc.flow.task_events_mgr import TaskEventsManager
     from cylc.flow.workflow_db_mgr import WorkflowDatabaseManager
-    from cylc.flow.flow_mgr import FlowMgr
+    from cylc.flow.flow_mgr import FlowMgr, FlowNums
 
 Pool = Dict['PointBase', Dict[str, TaskProxy]]
 
@@ -581,11 +581,7 @@ def spawn_successor_if_parentless(
                     not next_task.flow_nums
                     and not next_task.state.is_runahead
                 )
-                next_task.merge_flows(itask.flow_nums)
-                LOG.info(
-                    f"[{next_task}] merged in flow(s) "
-                    f"{','.join(str(f) for f in itask.flow_nums)}"
-                )
+                self.merge_flows(next_task, itask.flow_nums)
                 if retroactive_spawn:
                     # Did not belong to a flow (force-triggered) before merge.
                     # Now it does, so spawn successor, and children if needed.
@@ -1173,15 +1169,7 @@ def spawn_on_output(self, itask, output, forced=False):
             )
             if c_task is not None:
                 # Child already exists, update it.
-                if not c_task.flow_nums:
-                    # Child does not belong to a flow (force-triggered). Now
-                    # (merging) it does, so spawn outputs completed so far.
-                    self.spawn_on_all_outputs(c_task, completed_only=True)
-                c_task.merge_flows(itask.flow_nums)
-                LOG.info(
-                    f"[{c_task}] merged in flow(s) "
-                    f"{','.join(str(f) for f in itask.flow_nums)}"
-                )
+                self.merge_flows(c_task, itask.flow_nums)
                 self.workflow_db_mgr.put_insert_task_states(
                     c_task,
                     {
@@ -1776,3 +1764,34 @@ def match_taskdefs(
                     n_warnings += 1
                     continue
         return n_warnings, task_items
+
+    def merge_flows(self, itask: TaskProxy, flow_nums: 'FlowNums') -> None:
+        """Merge itask.flow_nums with flow_nums.
+
+        This also performs required spawning / state changing for edge cases.
+        """
+        # case 1: task has finished with incomplete outputs
+        # (we reset it to waiting and re-queue so it can run again as a task
+        # with complete outputs would)
+        if (
+            itask.state(*TASK_STATUSES_FINAL)
+            and itask.state.outputs.get_incomplete()
+        ):
+            itask.state_reset(TASK_STATUS_WAITING)
+            if not itask.state.is_queued:
+                self.queue_task(itask)
+            self.data_store_mgr.delta_task_state(itask)
+
+        # case 2: task does not belong to a flow (force-triggered no-flow).
+        # (we spawn the outputs complete so far to allow the flow to continue
+        # post merge)
+        # (note we don't do this if case 1 also applies)
+        elif not itask.flow_nums:
+            self.spawn_on_all_outputs(itask, completed_only=True)
+
+        # merge the flows
+        itask.merge_flows(flow_nums)
+        LOG.info(
+            f"[{itask}] merged in flow(s) "
+            f"{','.join(str(f) for f in itask.flow_nums)}"
+        )
diff --git a/cylc/flow/task_proxy.py b/cylc/flow/task_proxy.py
index 1f56814c52d..e054405ad75 100644
--- a/cylc/flow/task_proxy.py
+++ b/cylc/flow/task_proxy.py
@@ -439,6 +439,7 @@ def name_match(self, name: str) -> bool:
 
     def merge_flows(self, flow_nums: Set) -> None:
         """Merge another set of flow_nums with mine."""
+        # update the flow nums
         self.flow_nums.update(flow_nums)
 
     def state_reset(
diff --git a/tests/functional/spawn-on-demand/15-reflow-incomplete-outputs.t b/tests/functional/spawn-on-demand/15-reflow-incomplete-outputs.t
new file mode 100644
index 00000000000..1458e606fec
--- /dev/null
+++ b/tests/functional/spawn-on-demand/15-reflow-incomplete-outputs.t
@@ -0,0 +1,25 @@
+#!/usr/bin/env bash
+# THIS FILE IS PART OF THE CYLC WORKFLOW ENGINE.
+# Copyright (C) NIWA & British Crown (Met Office) & Contributors.
+# 
+# This program is free software: you can redistribute it and/or modify
+# it under the terms of the GNU General Public License as published by
+# the Free Software Foundation, either version 3 of the License, or
+# (at your option) any later version.
+#
+# This program is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+# GNU General Public License for more details.
+#
+# You should have received a copy of the GNU General Public License
+# along with this program.  If not, see <http://www.gnu.org/licenses/>.
+#-------------------------------------------------------------------------------
+
+# Check correct behaviour if a no-flow task is manually triggered just ahead of
+# the main flow.  See GitHub #4645
+
+. "$(dirname "$0")/test_header"
+set_test_number 2
+reftest
+exit
diff --git a/tests/functional/spawn-on-demand/15-reflow-incomplete-outputs/flow.cylc b/tests/functional/spawn-on-demand/15-reflow-incomplete-outputs/flow.cylc
new file mode 100644
index 00000000000..5428c8a24a3
--- /dev/null
+++ b/tests/functional/spawn-on-demand/15-reflow-incomplete-outputs/flow.cylc
@@ -0,0 +1,20 @@
+[scheduler]
+   [[events]]
+       expected task failures = 1/b
+
+[scheduling]
+    [[graph]]
+        R1 = """
+            a => b => c
+        """
+
+[runtime]
+    [[b]]
+        script = """
+            # test $CYLC_TASK_SUBMIT_NUMBER -gt 1
+            if [[ $CYLC_TASK_SUBMIT_NUMBER -eq 1 ]]; then
+                cylc trigger --reflow "$CYLC_WORKFLOW_NAME//1/a"
+                false
+            fi
+        """
+    [[a,c]]
diff --git a/tests/functional/spawn-on-demand/15-reflow-incomplete-outputs/reference.log b/tests/functional/spawn-on-demand/15-reflow-incomplete-outputs/reference.log
new file mode 100644
index 00000000000..434bf4f37e4
--- /dev/null
+++ b/tests/functional/spawn-on-demand/15-reflow-incomplete-outputs/reference.log
@@ -0,0 +1,7 @@
+Initial point: 1
+Final point: 1
+1/a -triggered off []
+1/b -triggered off ['1/a']
+1/a -triggered off []
+1/b -triggered off ['1/a']
+1/c -triggered off ['1/b']