JSFiddle - React, Tailwind, and code Playground

HTML

<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<input type="text" id="contract_year" placeholder="Contract" autocomplete="off">
<button type="button">Submit</button>
<div id="match_player_id"></div>

JavaScript

$('button').click(function(e) {
  e.preventDefault();
  
  console.log('Previous value:', localStorage.getItem('contractYear'))
  
  var contractYear = $('#contract_year').val();
  $('#match_player_id').html(contractYear);
  
  localStorage.setItem('contractYear', contractYear);
  console.log('New value:', localStorage.getItem('contractYear'))
});