diff --git a/server/src/main/java/org/elasticsearch/snapshots/RestoreService.java b/server/src/main/java/org/elasticsearch/snapshots/RestoreService.java
index b8fa8c6f1a9c8..49fd26c070af1 100644
--- a/server/src/main/java/org/elasticsearch/snapshots/RestoreService.java
+++ b/server/src/main/java/org/elasticsearch/snapshots/RestoreService.java
@@ -314,6 +314,12 @@ public ClusterState execute(ClusterState currentState) {
                                                                         currentIndexMetaData.getMappingVersion() + 1));
                                 indexMdBuilder.settingsVersion(Math.max(snapshotIndexMetaData.getSettingsVersion(),
                                                                         currentIndexMetaData.getSettingsVersion() + 1));
+
+                                for (int shard = 0; shard < snapshotIndexMetaData.getNumberOfShards(); shard++) {
+                                    indexMdBuilder.primaryTerm(shard,
+                                        Math.max(snapshotIndexMetaData.primaryTerm(shard), currentIndexMetaData.primaryTerm(shard)));
+                                }
+
                                 if (!request.includeAliases()) {
                                     // Remove all snapshot aliases
                                     if (!snapshotIndexMetaData.getAliases().isEmpty()) {
diff --git a/server/src/test/java/org/elasticsearch/snapshots/SharedClusterSnapshotRestoreIT.java b/server/src/test/java/org/elasticsearch/snapshots/SharedClusterSnapshotRestoreIT.java
index 1a1b886e0e373..d633493622dcd 100644
--- a/server/src/test/java/org/elasticsearch/snapshots/SharedClusterSnapshotRestoreIT.java
+++ b/server/src/test/java/org/elasticsearch/snapshots/SharedClusterSnapshotRestoreIT.java
@@ -116,6 +116,7 @@
 import java.util.function.Consumer;
 import java.util.function.Predicate;
 import java.util.stream.Collectors;
+import java.util.stream.IntStream;
 import java.util.stream.Stream;
 
 import static org.elasticsearch.cluster.metadata.IndexMetaData.SETTING_NUMBER_OF_REPLICAS;
@@ -3704,6 +3705,48 @@ public void testAbortedSnapshotDuringInitDoesNotStart() throws Exception {
         }
     }
 
+    public void testRestoreIncreasesPrimaryTerms() {
+        final String indexName = randomAlphaOfLengthBetween(5, 10).toLowerCase(Locale.ROOT);
+        createIndex(indexName, Settings.builder()
+            .put(SETTING_NUMBER_OF_SHARDS, 2)
+            .put(SETTING_NUMBER_OF_REPLICAS, 0)
+            .build());
+        ensureGreen(indexName);
+
+        if (randomBoolean()) {
+            // open and close the index to increase the primary terms
+            for (int i = 0; i < randomInt(3); i++) {
+                assertAcked(client().admin().indices().prepareClose(indexName));
+                assertAcked(client().admin().indices().prepareOpen(indexName));
+            }
+        }
+
+        final IndexMetaData indexMetaData = client().admin().cluster().prepareState().clear().setIndices(indexName)
+            .setMetaData(true).get().getState().metaData().index(indexName);
+        final int numPrimaries = getNumShards(indexName).numPrimaries;
+        final Map<Integer, Long> primaryTerms = IntStream.range(0, numPrimaries)
+            .boxed().collect(Collectors.toMap(shardId -> shardId, indexMetaData::primaryTerm));
+
+        assertAcked(client().admin().cluster().preparePutRepository("test-repo").setType("fs").setSettings(randomRepoSettings()));
+        final CreateSnapshotResponse createSnapshotResponse = client().admin().cluster().prepareCreateSnapshot("test-repo", "test-snap")
+            .setWaitForCompletion(true).setIndices(indexName).get();
+        assertThat(createSnapshotResponse.getSnapshotInfo().successfulShards(), equalTo(numPrimaries));
+        assertThat(createSnapshotResponse.getSnapshotInfo().failedShards(), equalTo(0));
+
+        assertAcked(client().admin().indices().prepareClose(indexName));
+
+        final RestoreSnapshotResponse restoreSnapshotResponse = client().admin().cluster().prepareRestoreSnapshot("test-repo", "test-snap")
+            .setWaitForCompletion(true).get();
+        assertThat(restoreSnapshotResponse.getRestoreInfo().successfulShards(), equalTo(numPrimaries));
+        assertThat(restoreSnapshotResponse.getRestoreInfo().failedShards(), equalTo(0));
+
+        final IndexMetaData restoredIndexMetaData = client().admin().cluster().prepareState().clear().setIndices(indexName)
+            .setMetaData(true).get().getState().metaData().index(indexName);
+        for (int shardId = 0; shardId < numPrimaries; shardId++) {
+            assertThat(restoredIndexMetaData.primaryTerm(shardId), equalTo(primaryTerms.get(shardId) + 1));
+        }
+    }
+
     private RepositoryData getRepositoryData(Repository repository) throws InterruptedException {
         ThreadPool threadPool = internalCluster().getInstance(ThreadPool.class, internalCluster().getMasterName());
         final SetOnce<RepositoryData> repositoryData = new SetOnce<>();