Is there a way to increase hair growth around my mouth (where no hair seems to grow at all)? (Photo)

Beard hair is a genetic trait similar to the color of your eyes and hair.  Hair transplant may be an option.

Your question does not say how old  you are but you appear young, less than 30. If you are less than 20 years old, you may not be fully done with puberty and the facial hair can continue to fill in. However, if this is a family trait, then this may be the norm for you. Minoxidil and Latisse are topical products that are approved for hair growth on the scalp and eyelashes, respectively. Some patients have tried these with variable success on other areas like the beard. There are many claims oby over-the-counter products in regards to hair growth but you are likely to be disappointed by those and I don't recommend wasting your money on them. A beard transplant may be feasible if it is really bothersome if you are an appropriate candidate.

All of those  hundreds of products out there that claim that they can fill in patches and make hair grow faster are fake and useless. they dont work . You need a scalp hair transplant to your beard ıf you wish more but important point is that you have to wait at least to 22-23 to have  full growth beard on your face ..you seems pretty young ! 

Many young men want to accelerate their beard growth and ask about it. It takes age (genetic triggers which occur in family lines) so if you want to find out when your beard will grow out, you need to find out when your father or grandfather started to grow their beard. Hormones should have kicked in nicely by the time a man reaches 18 but he must wait out his genetics as hormone alone are not responsible for the onset of beard grown. Beard transplants can be done when the young man is a bit older (over 25) if the beard has not grown in yet.