If you suspect that your partner is addicted to porn what should your do?

Consult therapist. I would suggest consulting with a therapist who has experience in dealing with porn and sex addiction. There are many resources for such treatment, including: http://www.Recoveryconnection.Org/pornography-addiction-treatment/ with such a therapist, you can discuss your concerns and receive support -- plus help planning intervention if it's needed. Your partner may resist this, though.
Other options. Check out these websites to help you end the porn addiction which leads to erectile dysfunction, anxiety, depression, relationship issues in many. http://www.purityispossible.com and http://www.drmajeres.com.