Referral after coffee chat

I've been networking for an industry specific boutique. it's very niche and they are a small firm. i had a great chat with someone at the director level(HS alum) who then referred me to an associate who had recently left(college alumni) as well as a recruiter. both of those went well, and the recruiter referred to me an associate. I haven't applied yet as the application just opened, but i would like to put down a referral. Would it be ok to email the director again and ask for a referral? if so, how could I go about doing that?