Obviously that depends entirely on all of the ingredients in the pudding – a list you didn't share with us.

explained elsewhere, kosher for Passover is a stricter subset of kosher that excludes most grains, and for a subset of people who keep kosher, excludes rice, legumes, corn, all their derivatives, and certain other foods. So puddings, so often thickened with corn starch, or sweetened with any amount of corn syrup, or containing soy lecithin are not going to be certified kosher for Passover.

Can you find a commercially produced pudding that meets all the requirements? Possibly, but it does seem unlikely, doesn't it? A glance at the sites of some of the leading kosher foods producers did not turn up a kosher-for-Passover pudding.

There are symbols that indicate foods that are kosher for Passover. You might be able to find a pudding that bears this symbol and lives up to that standard. If not, here's a recipe for Mum's English Matzo Pudding – a complete dessert on its own – that you might turn to as a last resort.