  In this article, we study the expanding nature of universe in the contest of
$f(R,L_m)$ gravity theory, here $ R $ represents the Ricci scalar and $ L_m $
is the matter Lagrangian density. With a specific form of $ f(R,L_m) $, we
obtain the field equations for flat FLRW metric. We parametrize the
deceleration parameter in terms of the Hubble parameter and from here we find
four free parameters, which are constraints and estimated by using $H(z)$,
$Pantheon$, and their joint data sets. Further, we investigate the evolution of
the deceleration parameter which depicts a transition from the deceleration to
acceleration phases of the universe. The evolution behaviour of energy density,
pressure, and EoS parameters shows that the present model is an accelerated
quintessence dark energy model. To compare our model with the $ \Lambda $CDM
model we use some of the diagnostic techniques. Thus, we find that our model in
$ f(R,L_m) $ gravity supports the recent standard observational studies and
delineates the late-time cosmic acceleration.
