Add Taxonomy Images in WordPress – without plugins https://yourblogcoach.com/how-to-add-taxonomy-images-in-wordpress/#Add_Taxonomy_Images_in_WordPress_-_without_plugins

functions.php

<?php
/**
 * ADD IMAGE META ON CATEGORIES
 * @from : https://yourblogcoach.com/how-to-add-taxonomy-images-in-wordpress/#Add_Taxonomy_Images_to_Default_Taxonomy_Category
 */
add_action( 'category_add_form_fields', 'add_category_image', 10, 2 );
/**
 * Add image field on category
 * @param $taxonomy
 * @return void
 */
function add_category_image ( $taxonomy ) {
	?>
	<div class="form-field term-group">

		<label for="image_id"><?php _e('Image', 'taxt-domain'); ?></label>
		<input type="hidden" id="image_id" name="image_id" class="custom_media_url" value="">

		<div id="image_wrapper"></div>

		<p>
			<input type="button" class="button button-secondary taxonomy_media_button" id="taxonomy_media_button" name="taxonomy_media_button" value="<?php _e( 'Add Image', 'taxt-domain' ); ?>">
			<input type="button" class="button button-secondary taxonomy_media_remove" id="taxonomy_media_remove" name="taxonomy_media_remove" value="<?php _e( 'Remove Image', 'taxt-domain' ); ?>">
		</p>

	</div>
	<?php
}

/**
 * Save Image Field
 */
add_action( 'created_category', 'save_category_image', 10, 2 );
function save_category_image ( $term_id, $tt_id ) {
	if( isset( $_POST['image_id'] ) && '' !== $_POST['image_id'] ){
		$image = $_POST['image_id'];
		add_term_meta( $term_id, 'category_image_id', $image, true );
	}
}

/**
 * Add Image Field in Edit Form
 */
add_action( 'category_edit_form_fields', 'update_category_image', 10, 2 );
function update_category_image ( $term, $taxonomy ) { ?>
	<tr class="form-field term-group-wrap">
		<th scope="row">
			<label for="image_id"><?php _e( 'Image', 'taxt-domain' ); ?></label>
		</th>
		<td>

			<?php $image_id = get_term_meta ( $term -> term_id, 'image_id', true ); ?>
			<input type="hidden" id="image_id" name="image_id" value="<?php echo $image_id; ?>">

			<div id="image_wrapper">
				<?php if ( $image_id ) { ?>
					<?php echo wp_get_attachment_image ( $image_id, 'thumbnail' ); ?>
				<?php } ?>

			</div>

			<p>
				<input type="button" class="button button-secondary taxonomy_media_button" id="taxonomy_media_button" name="taxonomy_media_button" value="<?php _e( 'Add Image', 'taxt-domain' ); ?>">
				<input type="button" class="button button-secondary taxonomy_media_remove" id="taxonomy_media_remove" name="taxonomy_media_remove" value="<?php _e( 'Remove Image', 'taxt-domain' ); ?>">
			</p>

			</div></td>
	</tr>
	<?php
}

/**
 * Update Image Field
 */
add_action( 'edited_category', 'updated_category_image', 10, 2 );
function updated_category_image ( $term_id, $tt_id ) {
	if( isset( $_POST['image_id'] ) && '' !== $_POST['image_id'] ){
		$image = $_POST['image_id'];
		update_term_meta ( $term_id, 'image_id', $image );
	} else {
		update_term_meta ( $term_id, 'image_id', '' );
	}
}

/**
 * Enqueue Media Library
 */
add_action( 'admin_enqueue_scripts', 'load_media' );
function load_media() {
	wp_enqueue_media();
}

add_action( 'admin_footer', 'add_custom_script' );
function add_custom_script() {
	?> <script>jQuery(document).ready( function($) {
			function taxonomy_media_upload(button_class) {
				var custom_media = true,
					original_attachment = wp.media.editor.send.attachment;
				$('body').on('click', button_class, function(e) {
					var button_id = '#'+$(this).attr('id');
					var send_attachment = wp.media.editor.send.attachment;
					var button = $(button_id);
					custom_media = true;
					wp.media.editor.send.attachment = function(props, attachment){
						if ( custom_media ) {
							$('#image_id').val(attachment.id);
							$('#image_wrapper').html('<img class="custom_media_image" src="" style="margin:0;padding:0;max-height:100px;float:none;" />');
							$('#image_wrapper .custom_media_image').attr('src',attachment.url).css('display','block');
						} else {
							return original_attachment.apply( button_id, [props, attachment] );
						}
					}
					wp.media.editor.open(button);
					return false;
				});
			}
			taxonomy_media_upload('.taxonomy_media_button.button');
			$('body').on('click','.taxonomy_media_remove',function(){
				$('#image_id').val('');
				$('#image_wrapper').html('<img class="custom_media_image" src="" style="margin:0;padding:0;max-height:100px;float:none;" />');
			});

			$(document).ajaxComplete(function(event, xhr, settings) {
				var queryStringArr = settings.data.split('&');
				if( $.inArray('action=add-tag', queryStringArr) !== -1 ){
					var xml = xhr.responseXML;
					$response = $(xml).find('term_id').text();
					if($response!=""){
						$('#image_wrapper').html('');
					}
				}
			});
		});</script> <?php
}


/**
 * Display Image in Column
 */
add_filter( 'manage_edit-category_columns', 'display_image_column_heading' );
function display_image_column_heading( $columns ) {
	$columns['category_image'] = __( 'Image', 'taxt-domain' );
	return $columns;
}

/**
 * Let’s display the value for this column against each term id.
 */
add_action( 'manage_category_custom_column', 'display_image_column_value' , 10, 3);
function display_image_column_value( $columns, $column, $id ) {
	if ( 'category_image' == $column ) {
		$image_id = esc_html( get_term_meta($id, 'image_id', true) );

		$columns = wp_get_attachment_image ( $image_id, array('50', '50') );
	}
	return $columns;
}

Now, you can display image on frontend :
$image_id = get_term_meta ( $term_id, 'image_id', true ); echo wp_get_attachment_image ( $image_id, 'full' );