New Defender's Study Bible Notes
3:13 his promise. All the promises of God, especially including His promise to return and complete His great work of redemption, will be fulfilled, though it seems to us to be long delayed (II Peter 3:4). The old cosmos will have been dissolved, its material elements having been converted temporarily into energy (light, heat, sound, etc.), but will then be made over again as a “new” (Greek kainos, meaning “fresh,” rather than “young in age”) cosmos, with all the age-long effects of sin and the curse forever removed (with the one exception of the lake of fire and its inhabitants—see notes on Revelation 20:10).
3:13 dwelleth righteousness. The new heavens and new earth will no longer harbor any remnants of sin and its effects, so will “remain” forever (note Isaiah 65:17; 66:22; also note Revelation 21:1-5).