Yes, pressure will increase. There are three factors at play here. (1) Gay-Lussac's Law. If the container has a fixed volume 1 Litre, even if there is no change to the molar ratio of gases, the pressure must increase in accordance with Gay-Lussac's Law. (2) The shift of equilibrium caused by the increase of temperature, as others correctly deduced, will favour the r.h.s. giving more products. (3) Lastly, the mole ratios of gases, 2 moles on the l.h.s. and 4 moles on the r.h.s. This means there is mechanical work done on the system in the forward reaction, which will inhibit the forward reaction somewhat, but pressure will still increase.
Some students may be wondering, if the enthalpy change is so large and positive in the forward reaction, how come the iodine trichloride spontaneously decomposes? Well, the entropy change in the forward reaction is +596 J per K per 2 moles of iodine trichloride. Remember ΔG = 0 when the system reaches equilibrium. Plug this data into the Gibbs Free Energy equation, ΔG = ΔH - TΔS = 0 you can predict roughly the temperature at which this experiment was conducted, and you get around T = 400 K. At 300 K iodine trichloride is a stable solid, it starts to decompose at 340 K.