It will be easy for you two to slip into a pattern of either talking endlessly about the past or actually trying to mentally best each other; either one will simply be an extension of the relationship you shared in a prior life. Back then you each worked hard to prove that you were smarter than the other. There may have been an ongoing competition between you, waged at the intellectual level, and that old, combative energy will be felt again in this life.
You may find yourself slipping into that old role without even realizing it, making fun of your partner when they misspeak or badgering them into proving their opinions and other assertions. If you two want to stay together long-term, you'll have to find a way to tone down that competitive edge and foster an atmosphere of openness and acceptance. Rather than making your partner feel nervous about speaking their mind, show them that you care about their feelings and ideas by listening carefully when they speak, without judgment. Remember that even little 'jokes' about their intelligence can be like barbs that get under their skin and mar their self-confidence. Speaking their mind and following where their thoughts lead them is an essential part of their evolutionary process in this lifetime, and if you inhibit them from doing so, you'll actually be inhibiting the karmic growth of their soul.