A party wall is one that is shared with a neighbouring property…
It’s unusual for it to be beneficial to insulate them, as there would usually be assumed to be heat balance between the two properties. This though assumes that the neighbouring property is heated, and that the walls fully overlap.
In the case of a recent Tactical Energy Project we recommended that the homeowner insulate their party wall. Why?

You’ll see form the picture that these semi-detached properties are off-set front to back and also in elevation. The client mentioned that they sometimes felt cold sitting on the sofa in the living room. We assessed that this was very likely due to the bottom 1.5 meters of party wall behind the sofa having the next door neighbours cold, ventilated sub-floor behind it. The same was true down the back corner of the property where the house extended beyond the neighbours.
When insulating a party wall, its important to find an installer using a product that has been certified for use in that situation. Not all cavity wall insulation systems have that certification, and if they’re not appropriately certified, they likely won’t come with an insurance backed guarantee.