  The theoretically predicted intrinsic spin relaxation time of up to 1 $\mu s$
in graphene along with extremely high mobilities makes it a promising material
in spintronics. In spite of extensive experimental studies of spin relaxation
and understanding of its precise mechanism, it is still unclear as to why the
spin lifetime in graphene is three orders of magnitude below the theoretical
predictions. Central to this discrepancy is the role of the local environment
including that of the underlying substrate. In this work, we use the
electronically rich platform SrTiO$_3$ and study its suitability in supporting
spin transport in graphene. We find spin relaxation time and length as large as
1.2 $\pm$ 0.1 ns and 5.6 $\pm$ 0.5 $\mu m$ respectively at 290 K in graphene on
SrTiO$_3$ using a non-local measurement scheme. We analyze the temperature
variation of the spin transport parameters in graphene and attribute the
temperature dependence of the spin transport parameters in graphene to spin
orbit coupling or structural phase transition in SrTiO$_3$. Furthermore, from
the gate dependence of the spin transport parameters, the relation between spin
relaxation time and momentum relaxation time is extracted; the Elliot-Yaffet
and D'Yakonov-Perel' spin relaxation rates are found to be of similar order.
