In your if statement you are checking if the element is checked, but in the DOM the element is not checked therefore it will not bind the event on the button.
Move the if statement inside the bind event.
$("#test-with-prop").on("click", function () {
if ($("input:radio[name=existingpartner]").is(":checked")) {
check = $("#mycheckbox").prop("checked");
if (check) {
alert("Checkbox is checked.");
} else {
alert("Checkbox is unchecked.");
}
}
});