Hosea 3:4

‘For the children of Israel will abide many days without king, and without prince, and without sacrifice, and without pillar, and without ephod or teraphim,'

Israel's desolate state would be indicated by the fact that she would be bereft of all outward symbols of her previous religious activity, and have no means of reaching out towards heaven. She would be in this state for ‘many days' (compare Hosea 3:3). ‘Without king and without prince' might indicate a looking back to the time when YHWH was Israel's king whilst their ruler was His nagid (in the case of Saul, David and Solomon). That would tie in with ‘YHWH their God and David their king' in Hosea 3:5. But then we might have expected nagid instead of sar for prince. Or it may have in mind that David and his sons (princes) had been Israel's intercessory priests ‘after the order of Melchizedek' (2 Samuel 8:18; Psalms 110:4). Now they would have no one to intercede for them. Alternately the thought is that they would have neither king or governor, and would be leaderless, with no one to mediate for them. They would be a subject people. The lack of sacrifice, pillar, ephod and teraphim indicates a lack of all means of approaching God, or even any gods. Sacrifices were common to all religions. Pillars could have in mind memorial pillars such as that erected by Jacob at Bethel, but it could also refer to the pillars which represented Baal in the high places. Ephod could refer to the High Priest's garment, but it could also refer to accoutrements used in idol worship. Teraphim were figurines seen as offering protection and as a means of divination, and were mainly connected with false worship and idolatry. They are always frowned on. It is these last which prevent us from seeing the references as being necessarily towards what was seen to be religiously acceptable. Just as Hosea's new wife was to have no relationships either good or bad, so Israel would be bereft of all familiar relationships with the divine, whether good or bad. What she had previously clung to she will lose.