What size hole do I need for cementing in 2.4m 120mm pine fence posts into clay soil?
Depends on frost depth, height, and strength requirements of fence.

We generally drill 8" holes for a 3.5" square post 6" below frost depth or 30" deep in our area.  Minimum depth if frost depth is not an issue I would say is 18" for a heavy clay.  Deeper is better than wider.  This is for fences upwards of 6' high.  Higher fences we would probably set a deeper minimum post depth.

If we had a 120mm round, we would probably stick with the 8" diameter hole, but if it was 120mm square, we might up size to 10" diameter to ensure enough concrete around the post for it to stay intact.

If we needed more lateral strength, we would up size the hole diameter if we did not go any deeper.

For holes that layout cannot be adjusted and are not in the center, we enlarge the hole as needed to make sure there is adequate concrete surrounding the post.