The class setting is only used in the admin and I thing that the question is about the front end of the site.
The best choice for this is to wrap your field output in a div and use it to target the p’s in it.
<div class="your-class-here"><?php the_field('your-field'); ?></div>
<style>
.your-class-here p {
/* your styles here */
}
</style>
