  In this paper we obtain a new lower bound on the Erd\H{o}s distinct distances
problem in the plane over prime fields. More precisely, we show that for any
set $A\subset \mathbb{F}_p^2$ with $|A|\le p^{7/6}$, the number of distinct
distances determined by pairs of points in $A$ satisfies $$ |\Delta(A)| \gg
|A|^{\frac{1}{2}+\frac{149}{4214}}.$$ Our result gives a new lower bound of
$|\Delta{(A)}|$ in the range $|A|\le p^{1+\frac{149}{4065}}$.
  The main tools we employ are the energy of a set on a paraboloid due to
Rudnev and Shkredov, a point-line incidence bound given by Stevens and de
Zeeuw, and a lower bound on the number of distinct distances between a line and
a set in $\mathbb{F}_p^2$. The latter is the new feature that allows us to
improve the previous bound due Stevens and de Zeeuw.
