A Tower Controller reported an aircraft on a Visual Approach was not coordinated with them as required in their Letter of Agreement with TRACON. The aircraft was too high to land and when maneuvering for their descent they came into conflict with another aircraft in the TRACON airspace.

Narrative

I was training a Controller local control. Aircraft X was 10 miles south of FXE talking to MIA Approach. MIA then flashed Aircraft X yellow for us to approve a visual. We approved the visual. However; MIA is still responsible per the LOA to coordinate via the shoutline verbally for any jet to be cleared south of the airport. If they do not coordinate Aircraft X should have been cleared north of the airport. Aircraft X was switched 1 mile west of the airport BUE northbound at 220 kts. I asked Aircraft X what their intentions were and if they were able to land; the pilot stated unable to land and they had to go northbound. They were too high and fast. Aircraft X then came in direct conflict with Aircraft Y 2 miles north of the airport at 018 ft. and Aircraft X was at 020 ft. I gave Aircraft X a traffic alert and turned the aircraft west bound. I then gave Aircraft X a landing clearance and he landed without incident. MIA needs to follow the loa and coordinate an IFR jet visual from the south.