diff --git a/planner/core/find_best_task.go b/planner/core/find_best_task.go
index c00d94cc10337..469922857525e 100644
--- a/planner/core/find_best_task.go
+++ b/planner/core/find_best_task.go
@@ -635,6 +635,10 @@ func compareCandidates(lhs, rhs *candidatePath) int {
 }
 
 func (ds *DataSource) isMatchProp(path *util.AccessPath, prop *property.PhysicalProperty) bool {
+	if ds.table.Type().IsClusterTable() && !prop.IsSortItemEmpty() {
+		// TableScan with cluster table can't keep order.
+		return false
+	}
 	var isMatchProp bool
 	if path.IsIntHandlePath {
 		pkCol := ds.getPKIsHandleCol()
diff --git a/planner/core/task.go b/planner/core/task.go
index c805f7b7718d6..a838de8704985 100644
--- a/planner/core/task.go
+++ b/planner/core/task.go
@@ -21,6 +21,7 @@ import (
 	"github.com/pingcap/failpoint"
 	"github.com/pingcap/tidb/expression"
 	"github.com/pingcap/tidb/expression/aggregation"
+	"github.com/pingcap/tidb/infoschema"
 	"github.com/pingcap/tidb/kv"
 	"github.com/pingcap/tidb/parser/ast"
 	"github.com/pingcap/tidb/parser/charset"
@@ -1039,6 +1040,62 @@ func (p *PhysicalTopN) canPushDownToTiFlash(mppTask *mppTask) bool {
 	return true
 }
 
+// For https://github.com/pingcap/tidb/issues/51723,
+// This function only supports `CLUSTER_SLOW_QUERY`,
+// it will change plan from
+// TopN -> TableReader -> TableFullScan[cop] to
+// TopN -> TableReader -> Limit[cop] -> TableFullScan[cop] + keepOrder
+func (p *PhysicalTopN) pushLimitDownToTiDBCop(copTsk *copTask) (task, bool) {
+	if copTsk.indexPlan != nil || copTsk.tablePlan == nil {
+		return nil, false
+	}
+
+	var (
+		tblScan *PhysicalTableScan
+		err     error
+		ok      bool
+	)
+
+	copTsk.tablePlan, err = copTsk.tablePlan.Clone()
+	if err != nil {
+		return nil, false
+	}
+	finalTblScanPlan := copTsk.tablePlan
+	for len(finalTblScanPlan.Children()) > 0 {
+		finalTblScanPlan = finalTblScanPlan.Children()[0]
+	}
+
+	if tblScan, ok = finalTblScanPlan.(*PhysicalTableScan); !ok {
+		return nil, false
+	}
+
+	// Check the table is `CLUSTER_SLOW_QUERY` or not.
+	if tblScan.Table.Name.O != infoschema.ClusterTableSlowLog {
+		return nil, false
+	}
+
+	colsProp, ok := GetPropByOrderByItems(p.ByItems)
+	if !ok {
+		return nil, false
+	}
+	if len(colsProp.SortItems) != 1 || !colsProp.SortItems[0].Col.Equal(p.SCtx(), tblScan.HandleCols.GetCol(0)) {
+		return nil, false
+	}
+	tblScan.Desc = colsProp.SortItems[0].Desc
+	tblScan.KeepOrder = true
+
+	childProfile := copTsk.plan().statsInfo()
+	newCount := p.Offset + p.Count
+	stats := deriveLimitStats(childProfile, float64(newCount))
+	pushedLimit := PhysicalLimit{
+		Count: newCount,
+	}.Init(p.SCtx(), stats, p.SelectBlockOffset())
+	pushedLimit.SetSchema(copTsk.tablePlan.Schema())
+	copTsk = attachPlan2Task(pushedLimit, copTsk).(*copTask)
+	rootTask := copTsk.convertToRootTask(p.SCtx())
+	return attachPlan2Task(p, rootTask), true
+}
+
 func (p *PhysicalTopN) attach2Task(tasks ...task) task {
 	t := tasks[0].copy()
 	cols := make([]*expression.Column, 0, len(p.ByItems))
@@ -1046,6 +1103,12 @@ func (p *PhysicalTopN) attach2Task(tasks ...task) task {
 		cols = append(cols, expression.ExtractColumns(item.Expr)...)
 	}
 	needPushDown := len(cols) > 0
+	if copTask, ok := t.(*copTask); ok && needPushDown && copTask.getStoreType() == kv.TiDB && len(copTask.rootTaskConds) == 0 {
+		newTask, changed := p.pushLimitDownToTiDBCop(copTask)
+		if changed {
+			return newTask
+		}
+	}
 	if copTask, ok := t.(*copTask); ok && needPushDown && p.canPushDownToTiKV(copTask) && len(copTask.rootTaskConds) == 0 {
 		newTask, changed := p.pushPartialTopNDownToCop(copTask)
 		if changed {