Because there is too much space in the grid for some words, eight cells are initially left empty. Once the grid is complete, solvers must find a way to fill the empty cells, keeping all entries as real words. The additional letters spell out a two-word final answer, which is my dream holiday destination.
All entries except 16 across are included in the UK Advanced Cryptics Dictionary (UKACD), searchable with Qat.
Across
1. Polish large rims of enormous coins (6)
4. Greek city state's second component area (6)
10. "French river passed centre of Reims", describes folk tradition (4)
11. Brazilian city's unending public disturbance (3)
12. Costa Rican volcano released gas, essentially having something to do with kidneys? (5)
14/36. Italy's banks turned in oddly directed, chilling material (3,3)
15. Saint Kitts at last standing by papers by United Nations backing exposed people (7)
16. Japanese city's new pop group (4)
17. Portuguese borders – Lisbon's last enclosure? (3)
19. German choral piece describing the ultimate runner (6)
21. Peruvian natives excelled, taking #1 in the event (2,4)
24. Ecuadorian capital – the government's property? (6)
26. Niger's in distress without constant smiles (5)
27. Georgia's a state? (3)
30. British novel for myself, about mother (4)
31. Swede's backers do perhaps become mean (6)
33. American filmmaker Anderson, upon retirement, becomes tailor (3)
35. Oman's capital with harsh smell (5)
36. (See 14 across)
37. Chinese ambassador conceals scar (4)
38. Congo's ordered to release 100 gorillas (5)
39. American baseball team's strange slang about the last in league (6)
Down
1. Finnish sled pullers not accepting their southern relative getting their straps? (5)
2. Scots bard crazy about first-class programmes (10)
3. Poles backing woman producing balances (5)
5. Greek temple for god containing rebuilt throne (9)
6. India's majority backing resistance's zest (4)
7. Yemen's premier supports everyone making a friend (4)
8. English city's empty bar is almost too large (7)
9. British capital's central part missing small lake (4)
13. Greek god obtains one sign in the sky (5)
17. Byzantine poets, Asian romantic (10)
18. North Korea's fourth women's novel (3)
20. German board game about large rodent making seafaring vessel (9)
22. Pakistani elite guard: "Entrances secure" (3)
23. UAE's constituents dismissed three leaders' payments (5)
25. Vietnamese extremists, draped in melancholy, being rescued (5)
28. India's breaking children's game up to show style of walking (4)
29. Vietnamese festival has new small portable shelters (5)
32. German city's unusual sense (5)
33. Chinese dynasty described by music with lyrics (4)
34. Hong Kong film director's court (3)
