You can add a change event listener to the select.

const input = document.querySelector('input');
const select = document.getElementById("shipping_option");
input.required = select.value === '1';
select.addEventListener('change', e=>{
  input.required = select.value === '1';
});

<select required name="shipping_option" id="shipping_option">
  <option selected value="1">1</option>
  <option value="2">2</option>
</select>
    

I have this select and this input

<input  type="text" name="input" placeholder="input">

How I can make this input required when the selected option is 1?