Left-side 扌 is the hand radical, the three-stroke compressed form of 手. It marks 接 as a hand-action verb - receiving, catching, picking up, joining. Same family as 打, 拉, 推, 抱; almost any verb you do with your hands gets this radical.
Right-side 妾 gives the sound (qiè → jiē, affricate shift). 妾 itself is 立+女 (a standing woman); the original 'receive a guest at the door' meaning carried a faint social register tied to attendants. Modern 接 is essentially pure phonetic borrow - the sound link is the active part.
