The first thing I would do is talk to the experts. In the past I've found either ringing the paint companies, e.g. Dulux
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or calling into a paint shop (Not a hardware/b&Q style shop) and asking them. e.g. in Pat McDonnells paints in Cork/Dublin (as an example). These people do paint all day long.
If at all possible, bring a picture of the gate with you.
The problem is there are numerous coatings that are "plastic" and different paints stick to different ones. Some require an undercoat, or Tie coat, some require etching or sanding. Some, e.g. vinyl guttering, are very difficult to get anything to stick to.
And whatever they recommend, ask if it is possible to get a sample pack of the suggested paint. Try it on a small area as per the instructions. (undercoat/sanding/wait times/overcoat times etc.) Once it is set, use a craft knife to make cross cuts on the painted piece. (you only need to do 2~3 inchs square. Stick a bit of duct tape on it and see if the paint comes off when you pull off the tape. If it comes off, the paint won't stick, if it doesn't, then you're good to go.
I once did this test on a boat, and believe, me, I was happy I hadn't gone and painted the whole boat as the top coat was incompatible with the undercoat and would have peeled off in weeks.