A simple pendulum of length l hangs from the ceiling of an...

In the frame of reference of the elevator, a pseudo force $m a_0$ acts on the pendulum bob in the upward direction, opposite to the downward acceleration of the elevator.

The true gravitational force $mg$ acts in the downward direction.

The net effective force on the bob is $F_{eff} = mg - m a_0 = m(g - a_0)$.

The effective acceleration due to gravity is $g_{eff} = g - a_0$.

The time period of a simple pendulum is given by $T = 2\pi \sqrt{\dfrac{l}{g_{eff}}}$.

Substituting the value of $g_{eff}$, we get $T = 2\pi \sqrt{\dfrac{l}{g - a_0}}$.