Yes, you can learn to drive here and get a Barbados licence.
The UK provisional licence means nothing here for cars.
The licence system is very much like the UK was maybe thirty years ago - so less emphasis on theory and more on practical.
The actual test can be seen as difficult, the testers take their profession seriously - people go fail driving out of the test centre gates.
If one already has a full licence from the UK it can be exchanged for a Barbados licence. Most people not here for a year get a short-term permit from the licensing authority or a car hire company who issue them on behalf of the government.