The post title is obviously a trick question. There isn’t a “right play” but there are many “wrong” plays. We currently have troops in Iraq “training” the Iraqi army, and it isn’t clear how long that deployment will remain tenable. It would certainly be insane to try and deploy any forces outside of Taji Military Complex as some sort of soundbite enhancer for the government.
The “less wrong” play would be stop trying to play at being a country that matters and focus on protecting New Zealand’s interests. There really isn’t much for us in the Middle East, unless you think building sheep farms in the desert is the height of foreign policy achievement. Where is the vision? Where is the quantifiable achievement for New Zealanders who live in New Zealand in the form of jobs, higher household incomes and greater standards of living?