How to write this conditional statement?

by

is_tag checks whether the page being displayed is the tag archive page for the named tag. It does not check whether the post in a Loop has that tag, which is what you ask: “…to show if the post has tag premium…”. For that you need has_tag

if has_tag( 'premium' ){ ?>
    <a href="https://wordpress.stackexchange.com/questions/125158/<?php the_permalink(); ?>" class="info"> Subscribe</a><?php
} else { ?>
    <a href="https://wordpress.stackexchange.com/questions/125158/<?php the_permalink(); ?>" class="info">Read More</a><?php
}

Note that has_tag requires the tag slug and not the tag name, hence the lowercase.