I'm 21 but I don't have thick moustache or beard. Will shaving help to increase growth? What are my options?

Your parents passed on their genes on to you.  They gave you the genes for balding or a full head of hair.  They gave you the genes for facial hair or no facial hair.  There is nothing you can do to grow more beard. Shaving will not increase hair growth.

Shaving does not increase beard growth. Facial hair growth patterns are strongly genetic. A hair transplant is a common option. 

Shaving will not help you, only time. Wait until you develop a mature beard and mustache. It took me until I was 25 for my beard to mature.