  Using the first law of thermodynamics, we propose a relation between the
system entropy ($S$) and its IR ($L$) and UV ($\Lambda$) cutoffs. In addition,
applying this relation to the apparent horizon of flat FRW universe, whose
entropy meets the R\'{e}nyi entropy, a new holographic dark energy model is
addressed. Thereinafter, the evolution of the flat FRW universe, filled by a
pressureless source and the obtained dark energy candidate, is studied. In our
model, there is no mutual interaction between the cosmos sectors. We find out
that the obtained model is theoretically powerful to explain the current
accelerated phase of the universe. This result emphasizes that the generalized
entropy formalism is suitable for describing systems including the long-range
interactions such as gravity.
