GeoDirectory stores custom field values in its own table for each post type, not in WordPress post meta, so get_post_meta() returns nothing for them. Use geodir_get_post_meta() with the listing ID and the field key:

$instagram = geodir_get_post_meta( $post_id, 'instagram', true );

The key is the Key setting of the field in Places > Settings > Custom Fields. In GeoDirectory v1 custom field keys started with geodir_, for example geodir_instagram. The upgrade to v2 removed that prefix, so use the key exactly as the field settings show it.

Get all fields of a listing at once

geodir_get_post_info() returns an object with every field of the listing, which is handy when you need several values:

$listing = geodir_get_post_info( $post_id );

if ( ! empty( $listing->instagram ) ) {
	echo esc_html( $listing->instagram );
}

On a listing detail page and inside GeoDirectory loops, the global $gd_post already holds that object for the current listing:

global $gd_post;

if ( ! empty( $gd_post->instagram ) ) {
	echo esc_html( $gd_post->instagram );
}

Showing a value without code

If you only want to display the value on a page, the GD > Post Meta block does it without PHP. Show set to “value (saved in database)” outputs the raw stored value:

[gd_post_meta key='instagram' show='value-raw']

See How can I display a custom field database value? for more on that.