Birthday Party by Arcadia

All across clues are normal, but the top row is unclued. 14D is thematic and unclued, although referenced by wordplay in one across clue. All other down clues are normal, except that the wordplay for one clue in each column leads to an extra letter which must be entered in the barred-off bottom row. Filling in the three grey cells will enable the top and bottom rows to match appropriately.

Across
13 Regions in Near East (5)
15 About third of a mile from Preseli to time control (6)
16 “Sure thing” created by leaders of Caernarfonshire Eisteddfod reps' team (4)
17 Lord King denying opening to mathematician (5)
18 Violin mostly reflecting professional skills (4)
19 Ancient eared bottle, price about a pound (7)
20 Wet one's whistle finally, drinking most of champagne (6)
21 Law Officer, flexible but never laughing (9)
22 Face claim after work (6)
24 Cuts away from scripture lessons by nonconformists (7)
26 See to clothe clergyman uprightly (7)
29 Case for S4C to introduce naked Eolian drinking songs (6)
31 Writing-desk of friend of Socrates in Republic (9)
33 Tense from delirious satori (6)
35 Waits on document signed at 22.00 beforehand (7)
36 Other source of Elan, twice skirting borders of Llanidloes (4)
37 Feet of one leaderless Disney deer (5)
38 Fluellen essentially kills exhausted deer (4)
39 Still 50-50 overs (6, two words)
40 Previously Italian bread had no buyers? (5)
41 Difference engine, uncovered, must hide its working (12)

Down
1 Note traces of injury in 25's crew (7)
2 Nasal explosions not previously raising awareness (6)
3 Move rapidly, as river Taff's first entering cwm (6)
4 Socially excludes damned bigots, with energy over time (11)
5 Snow White perhaps runs out of robust covering at Sam Tan's base? (11, two words)
6 Shape showing tenor for deserted shed (5)
7 Severe, ardent Anglican (6)
8 Airier points muddling qualities based on theoretical deduction (11)
9 Mat finally set back after slope in the gymnasts' vaulting aids (10)
10 Savory, say, served up regularly in Abernethy (4)
11 Briefly ruin enthusiasm (5)
12 Climb disused pig pen (4)
14 unclued (10, two words)
23 Glance away after surprise expressed about agreement (7)
25 Indian bosun's right to stop litter by rear of brig (6)
27 Powerless to contend with membraneous flap in space by intestines (6)
28 Rearing little piggy, suppressing its cry after the first wee-wee (6)
30 Refined lining of Welsh gold crowns borders (5)
32 Burns snubbed doctor of law (5)
33 Bashed out, striking son in cot (4)
34 According to nature penetrating humour doesn't exist (4)

Entries
To enter this competition, input your solution into the website at https://cc.vellender.com before 8th September 2025. The first correct entry drawn from the hat will receive a book from the Chambers range, which has been donated by Chambers.