The Psalmist is comparing; God’s reputation is very great in Judah and in Israel, and realises God’s name is great in Israel.
“In Judah is God known: his name is great in Israel.” Psalm 76:1
One place he’s just known, in another his name is great, he’s feared and is doing mighty.
He reckons, God shouldn’t only be known, but be feared for his mighty deeds, “Thou, even thou, art to be feared: and who may stand in thy sight when once thou art angry? (Psalm 76:7). Again he says, ”Thou art more glorious and excellent than the mountains of prey” (Psalm 76:4). I’ll comment on this beneath.
There was another situation again, “In Salem also is his tabernacle, and his dwelling place in Zion” (Psalm 76:2). God has two houses, but his dwelling place is only in the other. It is just not good enough for you to be His house that is well garnished, swept but remain still empty – without His presence. If that’s your situation, you’re a mountain of prey, he reckons, and things have to change right now.
Solomon said, “But I have built an house of habitation for thee, and a place for thy dwelling for ever.” (2 Chronicles 6:1-2) “Hearken therefore unto the supplications of thy servant, and of thy people Israel, which they shall make toward this place: hear thou from thy dwelling place, even from heaven; and when thou hearest, forgive” (2 Chronicles 6:21).
I’ve built this house for you Lord, even my whole being, so that you can dwell therein and hear my prayers and supplications. God’s reputation in this house should also be very great and mighty in glory.
However, this also is what will attract God’s presence for you, “Vow, and pay unto the Lord your God: let all that be round about him bring presents unto him that ought to be feared” (Psalm 76:11). All it means is engage him, or serve Him. “But to do good and to communicate forget not: for with such sacrifices God is well pleased.” Hebrews 13:16