As ever, great fun from Slormgorm.
A steady solve with a few clever misdirections, but nothing too challenging. Many thanks to Slormgorm!

ACROSS
1. Member of The Police responsible for the beat? (8)
FLATFOOT
5. A plank on the Queen Anne’s Revenge? (6)
ABOARD
Double definition
Queen Anne’s Revenge was the name of one of Blackbeard’s ships
10. Dead fast going around end of course (2,5)
AT PEACE
AT PACE (fast) going around [cours]E (end of)
11. Relative ignoring Republican in high spirits (7)
ELATION
[r]ELATION (relative, ignoring R (Republican))
12. Priest minister had to do away with? (9)
ELIMINATE
ELI (priest) + MIN (minister) + ATE (had)
13. One spotted around new restaurant primarily? (5)
DINER
DIE (one spotted) around N (new) + R[estaurant] (primarily) &lit
15. Jet in exercises over city close to Brighton (5)
PLANE
PE (exercises) over LA (city) + [Brighto]N (close to)
16. Beastly types make a mess of cabarets (8)
BEARCATS
(CABARETS)* (*make a mess of)
19. Large city? That might describe Havana! (3,5)
BIG SMOKE
Double definition
Havana also being a cigar
20. Spirit picked up in a foreign capital (5)
SEOUL
“SOUL” (spirit, “picked up”)
21. Some sot on Galliano is a state (5)
TONGA
[so]T ON GA[lliano] (some)
23. I’m a cheat about to wrap up northern plot (9)
MACHINATE
(I’M A CHEAT)* (*about) to wrap up N (northern)
25. Gas milliner gets after drop of Coca-Cola (7)
CHATTER
HATTER (milliner) gets after C[oca-Cola] (drop of)
27. Picture that’s about mother and her ruin? (7)
IMAGINE
I.E. (that’s) about MA (mother) and GIN (her ruin)
28. Swimmer crossing end of river channel (6)
TRENCH
TENCH (swimmer) crossing [rive]R (end of)
29. Awful tailor dressing nurse from the east? (8)
ORIENTAL
(TAILOR)* (*awful) dressing EN (nurse)
DOWN
1. Eruptions in trousers you quietly covered up (5-3)
FLARE-UPS
FLARES (trousers), U (you) + P (quietly) covered up
2. What helps one get a job interview is diligence (11)
APPLICATION
3. Excited fans like soprano’s eccentricity (9)
FLAKINESS
(FANS LIKE S (soprano))* (*excited)
4. Old and wicked character from Greece (5)
OMEGA
6. Tasteless debut of Love divides musical group (5)
BLAND
L[ove] (debut of) divides BAND (music group)
7. Excellent to drink medium-sized Bud in Paris (3)
AMI
AI (excellent) to drink M (medium-sized)
8. One who gives party outside beside river (5)
DONOR
DO (party) outside ON (besides) + R (river)
9. Bishop getting Australian Dame a drink (8)
BEVERAGE
B (bishop) + EVERAGE (Australian Dame)
14. Patriot Italians not in need of revolution (11)
NATIONALIST
(ITALIANS NOT)* (*in need of revolution)
16. Kids of the 1950s stealing large knickers (8)
BLOOMERS
BOOMERS (kids of the 1950s) stealing L (large)
17. Have a go at conservative criminal agitates (9)
CASTIGATE
C (Conservative) + (AGITATES)* (*criminal)
18. Adult getting short, beautiful woman a flower (8)
BLUEBELL
BLUE (adult) getting BELL[e] (beautiful woman, short)
21. Jazz fan upset by The X-Factor is silent (5)
TACIT
CAT< (jazz fan, <upset) by IT (the x-factor)
22. A jerk holding tenor in a storage space (5)
ATTIC
A TIC (a jerk) holding T (tenor)
24. One weeping about queen that’s on run (5)
CRIER
C (about) + R (queen) + I.E. (that’s) on R (run)
26. Beer in cut-price event? Heading off! (3)
ALE
[s]ALE (cut-price event, heading off)
Quite enjoyable. I wasn’t aware that a cat is a jazz fan. Google Maps thought I was mad when I wasted time trying to find the city of Lan close to Brighton! I also confidently entered COPELAND (drummer in The Police) for 1a, which I suspect might have been an artful misdirection?
A gentle offering to ease into the week with just a few parsings I wasn’t sure of ? thanks Teacow, for clearing up the mystery of ABROAD. Nor did I know this meaning of 3d, which I usually associate with ‘being unreliable’ but both were solved from definition/crossers.
Couldn’t help but laugh at FLARE-UPS, enjoyed BIG SMOKE (only in crosswords, mind) and the surface of IMAGINE. Likewise, 1a, but I was not fooled for a minute by this surface, good though it was. That said, it took me longer than it should have to snag the right sort of plod.
Thanks to Slormgorm and Teacow.
I found this quick tricky. For 20ac where does the E come from in SEOUL?
A pleasant start to the week and thanks to setter and blogger.
SM@3
‘Picked up’, means something ‘heard’ so the clue is a homophone : spirit (soul) sounding like Seoul.
Of course!
Thanks Diane
Geoff, I almost wrote in COPELAND as the first clue but refrained as I thought that it was too obvious. After I solved the very easy 4D, I realised that my caution was justified.
I must be older than you as I knew “cat” as a jazz fan. There is a club in Melbourne “www.pariscat.com.au” that features jazz and even has an upcoming tribute to Sting (aka Gordon Sumner of The Police -) who was born very close to where I was born – Gateshead for me; Wallsend for him.
My own opinion of jazz is that I like it just out of hearing range.
As to the crossword, I guessed 5A correctly but had not heard of “Queen Anne’s Revenge”
Pleasant puzzle, with a couple of good clues in FLATFOOT and especially FLARE-UPS in the top left corner to start off. There wasn’t anything too fiendish but I couldn’t see DONOR for the life of me; of course, I was thinking of the first two letters as the ‘party’ so couldn’t make sense of the ‘outside beside’ bit.
Clue of the day (and first &lit of the week) to DINER.
Thanks to Slormgorm and Teacow
Thanks for the blog, the usual set of neat and concise clues with a lot of variety.
Thanks Slormgorm for an entertaining crossword. Despite GK deficits (FLATFOOT, BIG SMOKE, Queen Anne’s Revenge) I was able to complete this puzzle without difficulty. My top picks were ELIMINATE, DINER, and AMI. Thanks Teacow for the blog.
All present and correct and speedy by my standards. I thought Flatfoot was hyphenated. I wrote Copeland in immediately for 1A without checking any of the crossers, but quickly realised my mistake.
LOI was Bluebell and Beverage took longer than it should’ve done, trying to fit Edna in the answer.
Really enjoyed this one. Thank you Slomgorm and Teacow. Had no idea on big smoke, but enjoyed flat foot after thinking copeland. Laughed at flare ups clue