Thank you to Flimsy. Definitions are underlined in the clues.
Across
1. Flower tax for business (8)
INDUSTRY : INDUS(the flow-er/river in India) + TRY(to tax/to make severe demands on).
5. Some wannabe longing to fit in (6)
BELONG : Hidden in(Some) “wannabe longing“.
9. Hospital department I trust completely (8)
ENTIRELY : ENT(abbrev. for “Ear, Nose And Throat”, a hospital department/specialty) + I + RELY(to trust/to depend on with full trust).
10. A bit each (6)
APIECE : A + PIECE(a bit/a portion).
12. Game not beginning – that’s fortunate (5)
LUCKY : “plucky”(game/eager and willing to do something brave) minus its 1st letter(not beginning).
13. Adult blasting to Saturn? (9)
ASTRONAUT : A(abbrev. for “adult”) + anagram of(blasting)TO SATURN.
14. Work out individual price (6)
FIGURE : Double defn: 1st: To reckon/calculate; and 2nd: A personality, as in “a figure in English politics”; and 3: A sum of money attached to something, as in “the property comes with a figure of a million pounds”.
16. Navy cutting fares for royal members (7)
PRINCES : N(abbrev. for “navy”) contained in(cutting) PRICES(fares paid for/cost of journeys on public transport).
19. Exemption from holding river back (7)
FREEDOM : FROM containing(holding) reversal of(… back) DEE(a river in Scotland).
21. Story that’s made up on purpose (6)
LEGEND : LEG(on/the half of a cricket field to the back of a batsman in position to receive the ball) + END(purpose/objective).
23. Print three forms – not hard to understand (9)
INTERPRET : Anagram of(… forms) Print three minus(not) “h”(abbrev. for “hard”).
25. Black horse – perhaps one in need of a groom (5)
BRIDE : B(abbrev. for “black”, as in chess notation, say) + RIDE(the means on/in which you take a journey, perhaps/say, a horse – and a horse might also need a groom to take care of it).
26. Broadcast is about god (6)
ISSUED : IS + reversal of(about) DEUS(Latin for god/deity).
27. Outer pane smashed, cutting tail of Great Dane? (8)
EUROPEAN : Anagram of(… smashed) Outer pane minus(cutting) last letter of(tail of) “Great“.
28. Actors removing soft coats (6)
LAYERS : “players”(actors in a play) minus(removing) “p”(abbrev. for “piano”, musical direction to play softly).
29. Fine champ in fact beaten (8)
DEFEATED : [F(abbrev. for “fine”) + EAT(to champ/to munch food noisily)] containing(in) DEED(an act, especially a criminal offence, as in “accessory after the fact”).
Down
1. Is about to deliver standards of perfection (6)
IDEALS : IS containing(about) DEAL(to deliver/to hand out).
2. Jack not working, having time for female (9)
DETECTIVE : “defective”(not working/faulty) with “t”(abbrev. for “time”) replacing(having … for) “f”(abbrev. for “female”).
Defn: …, in slang.
3. Keep protecting Republican? Get lost! (5)
STRAY : STAY(keep/remain in a specified state or position, as in “Keep silent!”) containing(protecting) R(abbrev. for a member of the Republican Party).
Defn: …/move away aimlessly from where one is supposed to be.
4. Free religious education – pray without a penny (7)
RELEASE : RE(abbrev. for “religious education”) + “please”(pray/preface to a polite request, as in “pray tell”) minus(without a) “p”(abbrev. for “penny”, the UK unit of currency).
6. Shooting up and hitting the wall (9)
EXPLODING : Double defn: 1st: …/rapidly increasing in extent or intensity; and 2nd: Going up/hitting? the wall/becoming very furious/angry.
I’m not sure of the 2nd, as “hit the wall” is when an athlete suddenly becomes exhausted in a long race, different from “go up the wall”.
7. Work on stage? (5)
OPERA : OP(abbrev. for “opus”, a musical or literary piece of work) placed above(on, in a down clue) ERA(a stage/a distinct period in history).
Defn: An example/? of a performance on stage.
8. Best girls primarily are revising before exam (8)
GREATEST : 1st letter of(… primarily) “girls” + anagram of(… revising) ARE plus(before) TEST(an exam).
“I am the …” boxer in the original boxers.

11. Check large sum of money that’s turned up (4)
STOP : Reversal of(… that’s turned up) POTS(large sum/a lot of money, as in “he left pots ofmoney”).
15. Boxers perhaps endure raw exchanges (9)
UNDERWEAR : Anagram of(… exchanges) ENDURE RAW.
Defn: An example of which/perhaps are boxer shorts.
17. Capacity to keep in Europe? (9)
CONTINENT : CONTENT(capacity of something/volume that something can contain, as in “the content of a beer bottle) containing(to keep) IN.
Defn: An example of which/? is Europe.
18. Approved of CIA file endlessly getting doctored (8)
OFFICIAL : Anagram of(… getting doctored) [OF CIA + “file” minus its last letter(endlessly)].
20. I’m worried regular characters are withdrawing a larger amount (4)
MORE : 1st, 3rd, 5th, 7th, and 9th letters(… regular characters) deleted from(… are withdrawing) “I’m worried“.
21. Large ship almost capsized touching eastern iceberg, perhaps (7)
LETTUCE : L(abbrev. for “large”) + reversal of(… capsized, in a down clue) “cutter”(a ship/sailing boat) minus its last letter(almost) plus(touching) E(abbrev. for “eastern”).
Defn: A variety of which/perhaps is the iceberg.

22. Drink for each knight on demand (6)
PERNOD : PER(for each, as in “What is the rate per hour?”) + N(abbrev. for “knight”, in chess notation) +OD(abbrev. for “on demand” in banking).

24. The empty pen is scratchy (5)
TESTY : “The” minus its middle letter(empty) + STY(a pen/enclosure for pigs, say).
Defn: …/bad-tempered.
25. What alcoholic wants cries of displeasure heard? (5)
BOOZE : Homophone of(… heard) “boos”(cries of displeasure/disapproval).
I wasn’t sure about 6 either. “Shooting up and hitting the ceiling” would have worked better.
I parsed 26ac differently: IS plus DEUS backwards (about). I think 7dn is indeed an &lit. clue. I share the concerns about 6dn.
Nonetheless, I enjoyed the puzzle and found the blog helpful. Thanks to both FLIMSY and Scchua.
Thanks for the blog, very entertaining. Your lettuce is definitely NOT an ICEBERG but does not matter.
A likeable solve from Flimsy to help forget an aching arm post-jab. Top picks were INDUSTRY, ASTRONAUT, UNDERWEAR and STOP. 5a was perhaps too evident and it’s ‘hit the roof’ for me but the sense was clear enough.
Thanks to Flimsy for the entertainment and Scchua for the fun show-and-tell.
Thanks to Flimsy and scchua. Entertaining. I was slowed down by starting with Scram, not STRAY, and parsed DETECTIVE but did not make the connection to Jack.
All good fun and I’ll join those with “concerns” about 6D. Learnt something new with OD in 22D.
I passed 21D as L (large) with cutter almost reversed and then E.
Thanks to Flimsy and Scchua.
DuncM@6, thanks. Oh dear, another fail. Blog corrected.
Hitting the wall is a common expression meaning to lose ones temper.
…..at least it was common in Northern Ireland fifty years ago
Thanks Flimsy, that was about right for me. It took awhile to get OPERA; I first tried “onset” (as a stage of a process) but I couldn’t parse it; I then tried “odeon” with “ode” being work + on, leading to stage (as in theatre) but ASTRONAUT erased that idea. Favourites were PRINCES, INTERPRET, and LETTUCE. Thanks scchua for the blog.
Many thanks to Flimsy and to scchua for the helpful blog.
Managed to finish correctly but with guesses at the much mentioned 6D and 21A (thought the cricket reference was a bit obscure for a global audience).
Pleasant enough. We had no quibbles about 6dn – if you take ‘explode’ in the sense of come to an end, possibly suddenly, then ‘hitting the wall’, as an athlete might use the expression, is coming to a sudden stop (and if taken literally would certainly mean that). At any rate we never gave it a second thought.
Plenty to enjoy, including ASTRONAUT (lovely &lit), RELEASE and UNDERWEAR.
Thanks, Flimsy and scchua.
Thanks Flimsy and scchua
Found this tougher going than normal from this setter for some reason, maybe a little distracted. Had issues with 6d too – having three attempts with EXPLOSIVE, then EXPLOSION before finally getting EXPLODING after the E and N wouldn’t fit into the story. Hadn’t heard of ‘hitting the wall’ meaning getting angry, only ‘hitting the roof’. This made LEGEND the last one in and ended up misparsing that – going with GEL as ‘that’s made’ turned around ‘up’ on END. Just forgot about the cricket LEG.
Liked both European clues at 27a and 17d.