This is a letters-latent cryptic crossword: an equal number of Across and Down clues have one extra letter in the wordplay that should be removed and noted down. These letters spell out a phrase which, interpreted correctly, indicate four words that the solver should find and highlight in the finished grid. Two Across clues and two Down clues have an extra word that should be removed before solving; these four words should indicate what the solver is to write in the sub-cells starting at $3$D and moving across. If extra help is needed it can be found nearby. All other clues are normal.
All words except proper nouns can be found in Chambers Dictionary. One word, unusually, has no accent in British English but has retained the accent in American English; the British version is preferred for this crossword.
Across: 1. Wrestling tournament remains in box office (5) 5. Military ruler's kind of wedding? (6) 11. Autumn bake I ate later to repay in kind (9) 13. Priest changing direction of line-up (4) 14. Not sober (i.e. sober after a fashion) (7) 15. Trap oddball (3) 16. Egyptian spirit (at the time) is lighter than Hydrogen ion (4) 18. German border river -- "Border A" lacking support (4) 19. Leaves Inverness' swirling gases (4) 20. Winter apples from Cyprus set standard (7) 21. A fib (French one) is repugnant (5) 24. Treat as an injury and put broken bone back in place (5) 26. Wood between cargo leads to damp under new nets aboard _Greek Empress_ (7) 29. Lady Lovelace (mechanical engineer) knight's wife (4) 31. To explain "magic" untie ends at any time (4) 32. Leone's little western post office company (4) 33. I put drink before Romanian bread (3) 34. Calling earnestly for e.g. Quahog social worker... (7) 36. ...Welsh chap unsettled Lucan (4) 37. Various dead -- no sign of Americans. Inoculate against smallpox! (9) 38. Lyric writers elaborate: it's dosh (6) 39. Skinner dismisses answer from one on a plane (5) Down: 1. Empty boasting: bishop ruined a good cigar (11) 2. Lofty melody that is written in Latin (6)* 3. Walthamstow necklace incorporates gem (5) 4. Spring eagles for example; they advocate hostility (5) 5. Blood relation up-ended bias (3) 6. Scottish intellect endures holding gas (5) 7. Torn-down zoo: site is unoccupied (6) 8. Germanium oxygen einsteinium takes in initial dopant producing 3s with crystal cavities (6) 9. Mother's sister takes pinch of salt with drug (it's not confirmed) (5) 10. Entire resin fermented for Rhine wine (11) 12. Get to know forerunners of linguistics education and rudiments of noology (5) 17. Live through loss of English from old tongue disease (5) 22. Intaglio grooves: essentially plain cavities (6) 23. Ernie smears oddly fundamental fluids! (6) 24. Short clergyman opens Apocrypha to right page (5) 25. Popular summer uproar: last of the plum wine you might see (6) 27. Race and be ahead without acceleration and lacking direction (5) 28. A hidden danger rising up separately (5) 29. Factotum is dead on arrival, left in middle of rurality (2-3) 30. Quell everyone Yau confused (5) 35. Friendly Swedish goblin brings up moral offence (3) * Originally this was "Lofty melody, for instance, written in Latin" but Deusovi correctly pointed out that I'd messed the clue up. [Note: Google Translate is less reliable than Google for some things.]