We present twelve new transit light curves of the hot-Jupiter TrES-3b observed during $2012-2018$ to probe the transit timing variation (TTV). By combining the mid-transit times determined from these twelve transit data with those re-estimated through uniform procedure from seventy one transit data available in the literature, we derive new linear ephemeris and obtain the timing residuals that suggest the possibility of TTV in TrES-3 system. However, the frequency analysis shows that the possible TTV is unlikely to be periodic, indicating the absence of an additional body in this system. To explore the other possible origins of TTV, the orbital decay and apsidal precession ephemeris models are fitted to the transit time data. We find decay rate of TrES-3b to be $bf dot{P_q}= -4.1 pm 3.1$ $ms$ ${yr}^{-1}$ and the corresponding estimated modified tidal quality factor of ${Q}^{}_{ast}$ $sim 1.11 times {10}^{5}$ is consistent with the theoretically predicted values for the stars hosting the hot-Jupiters. The shift in the transit arrival time of TrES-3b after eleven years is expected to be ${T}_{shift}sim 69.55 s$, which is consistent with the $RMS$ of the timing residuals. Besides, we find that the apsidal precession ephemeris model is statistically less probable than the other considered ephemeris models. It is also discussed that despite the linear ephemeris model appears to be the most plausible model to represent the transit time data, the possibility of the orbital decay cannot be completely ruled out in TrES-3 system. In order to confirm this, further high-precision and high-cadence follow-up observation of transits of TrES-3b would be important.
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