Yes, the Dominican Republic imposes several closed fishing seasons. By law, it is prohibited for anyone to fish, consume, or possess the following marine species during these designated time periods:
Lobster:  March 1- June 30
Crab:    March 1 - June 30
Conch:  July 1- Oct 31
This also means that these species should not be available for sale nor served at food establishments, markets, or other commercial locations during closed fishing months.
Fishing for parrotfish and sharks is strictly prohibited at all times, year round. Violating these laws will result in hefty fines and imprisonment.