Trimming nose hairs is perfectly okay and they will grow back eventually but just trimming the nose hairs will not make them grow faster.
After you trim your nose hair it can take around 4 to 6 weeks for your nose hairs to grow back completely so if you want to keep the nose hairs away you can trim the nose hairs more often.
Or use some nose hair wax to keep the nose hairs from growing back.
Just avoid plucking the nose hairs because not only is plucking your nose hairs painful but it can also lead to infection and damage your nose hair follicles which means they'll never grow back or may never grow back.
But if that's what you're wanting then plucking the nose hairs might be a good option but you might get an infection after you pluck the nose hairs.