The hair usually takes at least a month to grow in a recognized length and in case you have permed the hair the new grown hair will be in its original structure. In case you want to make the new grown hair straight to make it look same as the rest of your hair, there are lots of ways to do it.
First use the perm on the newly grown hair after it grows an inch long. Separate your hair as four parts and use the perm from root to newly grown hair ends. Avoid using the perm on the hair that has been already permed as it can make it break. Another option for straightening the new hair is with electric pressing comb. To use this tool, first mist the entire hair with heat protectant hairspray after washing it fully and use the pressing comb over the new hair without touching the scalp. You can also use a blow dryer for making the hair straight after misting the wet hair with heat protectant hairspray. Use the dryer along with comb attachment over the new hair to make it fully straight. Most of the people use ceramic iron for making their hair straight, but you must make sure to purchase a high quality iron to prevent hair damages. Use the ceramic iron on the hair section for about fifteen minutes after applying heat protectant hairspray on your hair till it becomes straight.