In the State of Tennesse, as a life tenant who has a life estate deed against a property what is there responsibility to pay against the property

I am unclear from the question as to what is meant by "pay against the property".  However, as some general guidelines, a life tenant is generally responsible for pay the real estate taxes against the property and to maintain the property (mowing, cleaning, etc.).  As to major repairs which may have a useful life longer than the life tenant (new roof, etc.) there should be a split between the life tenant and the owners of the remainder interest.  However, the apportionment of this amount is generally a matter of dispute.  Sometimes it is helpful to use Tennessee's mortality tables to compare the statistical interest of the life tenant (how old they are versus how long they are predicted to live) to the remainder owners in order to determine the split. This answer is for general informational purposes only and is not intended to constitute legal advice or a recommended course of action in any given situation. This answer is not intended to be, and should not be, relied upon by the recipient in making decisions of a legal nature with respect to the issues discussed herein. The recipient is encouraged to consult independent counsel before making any decisions or taking any action concerning the matters in this answer. This answer does not create an attorney-client relationship between the author (John R. LaBar)/Henry, McCord, Bean, Miller, Gabriel & LaBar, P.L.L.C. and the recipient.