  An exact cosmological solution of Einstein field equations (EFEs) is derived
for a dynamical vacuum energy in $f(R,T)$ gravity for
Friedmann-Lemaitre-Robertson-Walker (FLRW) space-time. A parametrization of the
Hubble parameter is used to find a deterministic solution of EFE. The
cosmological dynamics of our model is discussed in detail. We have analyzed the
time evolution of physical parameters and obtained their bounds analytically.
Moreover, the behavior of these parameters are shown graphically in terms of
redshift $`z'$. Our model is consistent with the formation of structure in the
Universe. The role of the $f(R,T)$ coupling constant $\lambda$ is discussed in
the evolution of the equation of state parameter. The statefinder and Om
diagnostic analysis is used to distinguish our model with other dark energy
models. The maximum likelihood analysis has been reviewed to obtain the
constraints on the Hubble parameter $H_0$ and the model parameter $n$ by taking
into account the observational Hubble data set $H(z)$, the Union 2.1
compilation data set $SNeIa$, the Baryon Acoustic Oscillation data $BAO$, and
the joint data set $H(z)$ + $ SNeIa$ and $H(z)$ + $SNeIa$ + $BAO $. It is
demonstrated that the model is in good agreement with various observations.
