No special access issues
Only a few people of Saba's small population (appr. 1915 people) know about the activity of climbing. So, I recommend you to explain what you are about to do to people that show interest. People are very welcoming of tourists but please show respect for the locals, most of the entire island is made up out of privately-owned land that in most cases you are allowed to cross. Just make sure to adhere to the common climbing ethics by leaving no traces. To elaborate, no littering, no chipping of rock, no campfires, no damaging vegetation and please brush of excess chalk and tick marks and park in designated areas.
The areas that have been developed are on accessible pieces of land that will not cause any issues of you visit them. But if you want to start and develop new climbing, I urge you to request permission to do so with the local landowners.