No, you do not need to apply sunscreen at night. Sunscreen is designed to protect your skin from the harmful effects of the sun's ultraviolet (UV) rays, which are not present at night. Applying sunscreen at night can actually be detrimental to your skin because the SPF in sunscreen is a large molecule that can clog pores and prevent your skin from breathing.
It is important to always wash off sunscreen before going to bed to allow your skin to repair itself and absorb other beneficial skincare products. Instead of applying sunscreen at night, focus on using a nighttime moisturizer that is formulated to hydrate and nourish your skin.