An experimental study of the delayed threshold phenomenon in a Vertical Extended Cavity Semiconductor Emitting Laser is carried out. Under modulation of the pump power, the laser intensity exhibits a hysteresis behavior in the vicinity of the threshold. The temporal width of this hysteresis is measured as a function of the modulation frequency, and is proved to follow the predicted scaling law. A model based on the rate equations is derived and used to analyze the experimental observations. A frequency variation of the laser around the delayed threshold and induced by the phase-amplitude coupling is predicted and estimated.