[CI][StableHLO] Auto-advance stablehlo fork (#14087)

Issue: https://github.com/openxla/iree/issues/12678
diff --git a/.github/workflows/advance_upstream_forks.yml b/.github/workflows/advance_upstream_forks.yml
index af1997b..6a297cd 100644
--- a/.github/workflows/advance_upstream_forks.yml
+++ b/.github/workflows/advance_upstream_forks.yml
@@ -79,3 +79,25 @@
           github_token: ${{ secrets.WRITE_ACCESS_TOKEN }}
           branch: master
           repository: iree-org/iree-tf-fork
+
+  advance_stablehlo-fork:
+    name: "Advance stablehlo-fork"
+    runs-on: ubuntu-20.04
+    steps:
+      - name: Checking out repository
+        uses: actions/checkout@8f4b7f84864484a7bf31766abe9204da3cbe65b3 # v3.5.0
+        with:
+          token: ${{ secrets.WRITE_ACCESS_TOKEN }}
+          repository: iree-org/stablehlo
+          ref: main
+
+      - name: Pull from upstream
+        run: |
+          git remote add upstream https://github.com/openxla/stablehlo.git
+          git pull --ff-only upstream main
+      - name: Pushing changes
+        uses: ad-m/github-push-action@40bf560936a8022e68a3c00e7d2abefaf01305a6 # v0.6.0
+        with:
+          github_token: ${{ secrets.WRITE_ACCESS_TOKEN }}
+          branch: main
+          repository: iree-org/stablehlo