How to add a class to term

Could this be what you’re looking for; first get the query string for alp and make a conditional statement every item in the loop against the query string alp

$selected_slug = $_GET['alp'] ? $_GET['alp'] : '';
$alp_class="";

$alp_list = get_terms(array( 'taxonomy' => 'alphabets','orderby' => 'name', 'hide_empty' => false ) );

foreach ( $alp_list as $alp ) {
    if($selected_slug === $alp->slug) $alp_class="active";

    printf('<a href="https://wordpress.stackexchange.com/questions/272025/%1$s/?s=%2$s&section=member_list&alp=%2$s&submit=search" class="%3$s">%4$s</a><br/>', get_bloginfo('url'), $alp->slug, $alp_class, $alp->name);
}

Updated code to add the active class on the link.

Let me know if that works.