Navigation links to posts in current term shortcode

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Have you tried to echo get_previous_post_link as this is what is called when you set function previous_post_link.

function fivehats_previous_post() {
// You need to echo it out for it to display in the page
echo get_previous_post_link( '%link', '%title', TRUE, ' ', 'property-category' );
}
add_shortcode( 'fh_prev', 'fivehats_previous_post' );