Clues marked with * have a shared unstated definition AND a shared unstated (and somewhat unusual) cryptic instruction as well!

Across:
   7. Came before getting upset re tepid sex! (10)
   9. Its previous leader's vanquished * (4)
  10. Cover article in promotional text (6)
  11. Best dismissed, caught by young lady (8)
  12. Saddled by cursed administrative "mandate", ... * (5)
  13. ... place war calls home: unjust mandate, barbaric invasion, barricades! * (9)
  14. 20 across backed by Gnosticism (3)
  15. May sent out forgiveness (7)
  17. Fellows holding onto every last bit of these wartorn strips (7)
  20. 14 across backed by feudalism (3)
  21. Lunatic led in last and put in power (9)
  23. South pursued independence, creating delineation * (5)
  26. Mac's hair arranged to give personal appeal (8)
  27. Geometry brought them fame (strictly notated) * (6)
  28. Lacking energy badly, the thirds give up (4)
  29. Exhibits how species evolved (10)
Down:
   1. Compact spot under the pagola at very ends (6)
   2. Good codeine arranged as the 1 of 6 granted 15 for it (8)
   3. Land with Sabratha's city ramparts * (5)
   4. Turn of phrase inspiring article as empire carved up by 1 of 6 (7)
   5. Satisfy visitor with cut of meat (6)
   6. Where IOC is based (in city in California, USA) gets 22.5 degrees (8)
   8. Took a long time to act decisively, but did when conquering that place (8)
  12. Somewhere to soak diseased part (3)
  13. Sleeping approximately forty fifths, which helps when walking a tightrope (3)
  14. Some 15 list saved, their efforts valued by public figures (8)
  16. Cumin she prepared for a drug user's cravings (8)
  17. What his 14 across calls him when David misses six (3)
  18. Instruments in country music always get allowed seven isolated seconds (8)
  19. In which one might bathe one's unhealthy part (3)
  20. Locals getting rebuffed because paying visitors enshrined * (7)
  22. The outer bird, cooking 'nested' oddity * (6)
  24. Bowed, powerless, thirsting (6)
  25. European agents say people visit * (5)