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Using a 3D General Circulation Model, the Unified Model, we present results from simulations of a tidally locked TRAPPIST-1e with varying carbon dioxide CO2 and methane CH4 gas concentrations, and their corresponding prescribed spherical haze profiles. Our results show that the presence of CO2 leads to a warmer atmosphere globally due to its greenhouse effect, with the increase of surface temperature on the dayside surface reaching up to ∼14.1 K, and on the nightside up to ∼21.2 K. Increasing presence of CH4 first elevates the surface temperature on the dayside, followed by a decrease due to the balance of tropospheric warming and stratospheric cooling. A thin layer of haze, formed when the partial pressures of CH4 to CO2 (p CH4/ p CO2) = 0.1, leads to a dayside warming of ∼4.9 K due to a change in the water vapour H2O distribution. The presence of a haze layer that formed beyond the ratio of 0.1 leads to dayside cooling. The haze reaches an optical threshold thickness when p CH4/ p CO2 ∼ 0.4 beyond which the dayside mean surface temperature does not vary much. The planet is more favourable to maintaining liquid water on the surface (mean surface temperature above 273.15 K) when p CO2 is high, p CH4 is low, and the haze layer is thin. The effect of CO2, CH4, and haze on the dayside is similar to that for a rapidly rotating planet. On the contrary, their effect on the nightside depends on the wind structure and the wind speed in the simulation. [ABSTRACT FROM AUTHOR]