Have her read read read! This forum, other web resources, printed books on the subject.
Have you communicated to her how exactly you feel your relationship with her has been enhanced? Many established couples experience a lovely NRE spill-over, improving their communication, sex-life etc.
One idea to improve the security she feels in your relationship; find out what are your love languages. I, for one, place the highest value on Acts of Service, whereas my partners might appreaciate Gifts, Physical Touch or Quality Time more. If I try to communicate that I care through the one love language I am most proficient in, for example by doing the dishes, my partner who values touch or time might sulk on the sofa and wonder why I think doing the dishes beats spending cuddle-time with them.
Me: bi female in my twenties