In principle it should decrease if you mean the fluorescence of the dot, not that of the trap. If the decay rate of the dot fluorescence without trap is K (thus lifetime of the dot fluorescence without trap is T = 1/K), and the rate of trapping is Ktr, that the total decay rate of fluorescence in the presence of the trap will be K + Ktr, thus fluorescence decay time in the presence of trap will be Ttr = 1/(K + Ktr), thus lifetime with trap will be K/(K + Ktr) of the lifetime without dot.

What Losytskyy says is correct. One way to be more confident that what you are seeing is trapping is to correlate changes in fluorescence lifetime with those in fluorescence quantum yield (or intensity). If the quantum yield and lifetime have both reduced upon some change to the quantum dot, it is likely you have introduced a defect that acts as a trap. 

Something to be cautious of is that not all traps recombine non-radiatively. Trap emission can yield a long lived component to the fluorescence. However, this emission typically occurs at lower energy; for example, below the quantum dot excitonic emission peak. So it's important to make sure you are measuring the quantum dot lifetime at the emission wavelength of interest.

Value Ttr = 1 / (K + Ktr) is not accurate, because the presence of traps leads to bimolecular fluorescence quenching. As a result, the time of fluorescence in the presence of the traps Ttr depends on the concentration of traps Сtr, since the velocity ktr is the second order rate constant. Thus we have Ttr = 1 / (k +Ctr*ktr).

When I wrote I thought of a trap that is a part on quantum dot (e.g. some doppant). If the trap is separately dissolved quencher, I aggree with Vladimir S. Pavlovich.

@ Paul D Cunningham, Dear sir... could you pls provide some reference papers or book ?

In my work I found average lifetimes of QDs are proportional to the presence of surface defects. Here the surface defects gives fluorescence and the average lifetime measured via TCSPC device. Is that contradictory?