Every level beyond L3 has certain gateway skills that most gyms require before they will move a girl up to the next level, even if the girls has exceeded the score set by USAG to allow mobility to the next level. Some of these skills are notoriously difficult to learn for many gymnasts. Here's a very partial list of skills that often cause trouble:
L4: kip on bars, going over the table on vault, cartwheel and handstand on beam
L5: free hip on bars, flyaway on bars, BWO or other backwards skill on beam, tucks on floor
L7: giants (some gyms require them) on bars, acro series on beam
L8: flipping vault (again, not strictly necessary but some gyms require), pirouette or B release on bars, twisting on floor, upgrading acro on beam
L9: flipping vault sufficiently upgraded, release on bars, double back dismount on bars, C tumbling on floor, acro on beam, flip on beam
L10: upgrading all events to include enough Cs and connections!