I do not know if this can be achieved with the public API. If there is you SHOULD prefer that solution to the one that I present below.
ActivityExecution execution = ...;
ExecutionImpl executionImpl = (ExecutionImpl) execution;
ActivityImpl activityImpl = executionImpl.getActivity();
Map<String, Transition> transitions = activityImpl.getOutgoingTransitionsMap(); // the leaving transitions, keyed by transition name