The 1807 Act of Parliament defined the African slave trade as including any trade in persons occurring in the New World, also. It was explicitly illegal to take someone from the British Caribbean to the United States as a slave and vice-versa, or to transfer them around the colonies of the British Caribbean. To quote from the 1807 Act:

it shall be unlawful for any of His Majesty's Subjects, or any Person or persons, resident in this United Kingdom, or in any of the Colonies, Territories, or Dominions thereunto belonging or in His Majesty's Possession or Occupation, to carry away or remove, or knowingly and wilfully to procure, aid, or assist in the carrying away or removing, as Slaves, or for the purpose of being sold, transferred, used, or dealt with as Slaves, any of the Subjects or Inhabitants of Africa, or any Island, Country, Territory, or Place in the West Indies, or any part of America whatsoever

Claims have been made in the past that slave trading continued in huge quantities after the 1807 Act. Whilst it is certainly true that the British government does not really take up anti-slavery enthusiastically as a moral struggle until the 1840s, and enforcement of the ban on the trade was haphazard in its early days, we have no evidence for the practice continuing in the US or the British Caribbean in a significant way after 1807. Such claims that it did are usually based on rumour or anti-slavery campaigners making fanciful claims that the Southern slave population was only growing due to thousands and thousands of illicit imports every year. Though about 10,000 people are thought to have arrived between 1809 and 1829 on British or American vessels, that pales in comparison to the average 44,000 who arrived every year between 1785 and 1807. Records for arrivals after 1829 are sparse, consistent with increasing hostility towards slavery as an institution in Britain from the 1820s onwards (the first legislative recognition that slaves should have certain basic rights and protections comes as early as 1823 in Britain).

And though some trading did continue, it is more likely that these were ships operating illicitly out of Africa and bringing slaves directly from there, rather than ferrying them between colonies. The United States at this time had a growing slave population but also a growing demand for labour, feeding a thriving internal slave market; there was little incentive to engage in a more expensive, risky and illegal practice of selling slaves to the Caribbean, and the Caribbean had concerns about maintaining its slave population after the end of the trade (though there was inter-colonial trade before abolition). And of course, though enforcement was even more haphazard than in Britain, the United States itself also outlawed the slave trade in 1807, meaning English-speaking North America was truly a no-go zone for all legal trading.

What we do have evidence of is some very limited trading in activity between the British colonies in the region, the legality of which is not always clear (is it slave trading if an owner travels from Jamaica to Barbados and then sells their slaves?). It was, in any event, a greatly diminished practice that does not compare to the intercolonial trade pre-1807 in any meaningful sense. The 1807 Act for all intents and purposes greatly diminished and eventually allowed for the final dismantling of the slave trade in all of its forms in English-speaking North America, except for the internal slave trade in the United States which continued to thrive and grow right up until the Civil War.