Pursuant to Court Rule 2:2-4, a motion for leave to appeal is granted only in the interest of justice. The problem is, however, that there is no precise definition of the "interest of justice". Experienced appellate lawyers gain an understanding of what it means to be in the interest of justice for purpose of an interlocutory appeal.
The Appellate Division has stated:
[W]e may grant leave to appeal where some grave damage or
injustice may be caused by the order below, such as may occur
when the trial court grants, continues, modifies, refuses or
dissolves an injunction, appoints a receiver or refuses an order
to wind up a pending receivership or to take the appropriate
steps to accomplish the purposes thereof, such as directing a
sale or other disposal of property held thereunder. We may also
be induced to grant leave where the appeal, if sustained, will
terminate the litigation and thus very substantially conserve the
time and expense of the litigants and the courts, as in the case
where the order attacked determines that the court or agency
below has jurisdiction of the subject matter or person.
Mandel, New Jersey Appellate Practice, ch. 10:2-1 (Gann 2011) (citation omitted).
For a detailed explanation of the "interest of justice" standard and how it has been applied since the court rules were revised in 1969, see chapter 10:2 of Gann Law Books's New Jersey Appellate Practice.
Mandel, New Jersey Appellate Practice (Gann Law Books 2011):

Mandel, New Jersey Appellate Practice (Gann Law Books 2010):

Mandel, New Jersey Appellate Practice (Gann Law Books 2009):
(COMING SOON)
Mandel, New Jersey Appellate Practice (Gann Law Books 2008):
