If king Saul killed all of the Amalekites except for Agag, and Amalek only continued since he impreganted a woman in prison before Shmuel killed him, then from where did the Amalek army that took captive the wives and children of Dovid and his men in Samuel I Ch 30 v1 onwards come from? This was still during Saul’s lifetime and he only ruled for less than 3 years?
ב"ה Shalom It seems that the answer is in the Pasuk itself in Shmuel (15:7), that Shaul killed only those found within specific boundaries. I found a few commentators who support this idea. Therefore, the Amalakites that David encountered were from those out of those boundaries. There are also midrashim which suggest that some of the Amalakites were able to disguise themselves through sorcery, and thereby were also able to evade Shaul. Others suggested that some fulfilled the seven laws of Noach so they were no longer categorized as those who were supposed to be wiped out. However, later they turned to their old ways and once again attained the status of amalakites. All the best