Schwinn runabout trailer/seatpost attachment
You need a seatpost shim, with an inner diameter that matches your existing seatpost, and an outer diameter that matches the inner diameter of the clamp.  Any decent bike shop will have these.

The measurement of your seatpost should be stamped into the metal - just pull the seatpost out, and it will be written below the minimum-insert line.

There is a shim for every combination of sizes - and you can get them in plastic or aluminium or steel or carbon fibre.  For your situation, a plastic shim would probably be fine, but I'd still prefer a metal one.  

Examples (not a recommendation)  https://hollandbikeshop.com/en-gb/bicycle-saddles-seatposts/seatpost-shim/