I completed all but 4dn, 18ac and 21dn in 28 minutes but then had a mental block and needed that time again to come up with the remaining answers, finally resorting to aids for 21dn. I'm still wondering whether to cry "foul!" over that one as both ways into the clue require specialist knowledge of the same subject. For Shakespeare scholars it would probably be a write-in but lesser mortals have to take their chance. I reached the point where I didn't care any more and just wanted to move on. Here's my blog...
As usual definitions are underlined in bold italics, {deletions are in curly brackets} and [anagrinds, containment, reversal and other indicators in square ones]
Across
1
In winter covering simple game absorbs silly cow (7)
SNOWCAP - SNAP (simple game) contains [absorbs] anagram [silly] of COW
5
Epic call to the States that’s endless (7)
HOMERIC - HO (call), {a}MERIC{a} (the States) [endless]
9
Stupid not to have opening near the tail (3)
AFT - {d}AFT (stupid) [not to have opening]. A bit of a loose definition here, I feel, as "aft" specifically refers to the stern of a ship which would never in any circumstances be called "the tail", so one has to go via another word such as "back" or "rear" to match the definition with the answer. On edit: Thanks to mct for pointing out that "aft" also applies to aeroplanes so "tail" is fine. I should have checked before sounding off because SOED has: Nautical & Aeronautics. In or near or to or towards the stern or tail.
10
Holding off briefly, go on green traffic signal, and make to race away (3,2,6)
PUT TO FLIGHT - PUTT (go on green - golf), OF{f} [briefly], LIGHT (traffic signal)
11
Ship that is carrying good clothing (8)
LINGERIE - LINER (ship), containing [carrying] G (good), IE (that is - id est)
12
Debrief of work in restaurant (4-2)
WASH-UP - Two meanings. I learned the first one quite late in my working life along with many other unnecessary modernisms that people sling around to make themselves feel trendy and with-it.
15
Despicable type, little open to love? (4)
TOAD - TAD (little) contains [open to] 0 (love)
16
Those labouring on jumbo maybe bought drinks and boasted after finally finishing (6,4)
GROUND CREW - {finishin}G [finally], ROUND (bought drinks - drinks that have been bought), CREW (boasted). In terms of air travel as indicated by "on jumbo" one might be more likely to think of cabin crew or pilot officers, but of course the ground crew work on a plane in another sense and get it ready for take-off.
18
Holy Office is impertinent but no end weird (10)
PRIESTHOOD - PRIES (is impertinent), THO' (but), OD{d} (weird) [no end]
19
The legend of Hop-o’-my-Thumb (4)
MYTH - Hidden in [of] {hop-o'-}MY-TH{umb}
22
Abscond, so busy with one’s feet? (3,3)
RUN OFF - If one is so busy one might be said to be "run off one's feet"
23
Man with pasturage rights is our age, almost (8)
COMMONER - COMMON ER{a} (our age) [almost]
25
Don’t address David familiarly, we are told, and don’t give up (5,3,3)
NEVER SAY DIE - DIE sounds like [we are told] "Dai", a familiar form of David in some parts
27
School leavers’ destination? One to France, one to Rome once (3)
UNI - UN (one, to France), I (one, to Rome once). "Yew-knee" - a ghastly modernism for "university". In my less tolerant moments I am tempted to think that anyone who calls it this should not be permitted to attend one.
28
Mine’s best chance to refuel (3,4)
PIT STOP - PIT' S (mine's), TOP (best)
29
Determination to have another go at puzzle? (7)
RESOLVE - Two meanings with the second one pronounced "re-solve"
Down
1
Bulb very bright at last across room (7)
SHALLOT - SO (very) + {brigh}T [at last] contains [across] HALL (room)
2
Showing off nine tattoos newly created (11)
OSTENTATION - Anagram [newly created] of NINE TATTOOS
3
Manager retains power element (6)
COPPER - COPER (manager) contains [retains] P (power)
4
Right attitude turns up in irregular style of government (10)
PATRIARCHY - R (right) + AIR (attitude) reversed [turns up] in PATCHY (irregular)
5
Trap / pirate chief (4)
HOOK - Two definitions. The pirate Captain in Peter Pan.
6
Non-English dinners should include fat birds (8)
MALLARDS - M{e}ALS (dinners) [non-English] contains [should include] LARD (fat)
7
Scrap / paper (3)
RAG - Two definitions
8
Relish getting out the fifth answer with tool (4-3)
CATS-PAW - CATS{u}P (relish) [getting out the fifth - letter], A (answer), W (with). "Catsup" as a variation of "catchup" or "ketchup" is a new one on me, although I see it has been mentioned here in despatches a couple of times without actually appearing as an answer. According to one of the usual sources it's principally an American term. It sounds somewhat unappetising to me as I'm aware of "cat up" as a dialect expression meaning to vomit.
13
Poppy for one gives a regularly-produced poetry book? (5,6)
HARDY ANNUAL - A definition by example and a cryptic hint with reference to the writer Thomas HARDY plus ANNUAL (regularly-produced book). Wiki advises that Hardy considered himself principally as a poet although I only know of him as a novelist.
14
Not acceptable to be shot stealing old car (3,2,5)
OUT OF ORDER - OUTER (shot) containing [stealing] O (old) + FORD (car). An "outer" is a shot in archery and other target sports which hits the outer circle of the bull's-eye.
17
Approving being in a comedy sketch is to invite trouble (3,3,2)
ASK FOR IT - A, FOR (approving) in SKIT (comedy sketch)
18
Briefly trim and lightly cut vegetable (7)
PARSNIP - PAR{e} (trim) [briefly], SNIP (lightly cut)
20
She’s admired a couple of drugs (7)
HEROINE - HEROIN (drug #1), E (drug #2)
21
Shakespearean Lord’s appearance in first word of his play (6)
AMIENS - MIEN (appearance) in AS (first word of his play - with "his" referring back to the Shakespearean Lord). I don't like this clue at all as both ways in require more than a passing knowledge of the same subject. There must be hundreds of Lords in Shakespeare so the most likely route to the answer is by recognising the name from enumeration and checking letters if one happens to know of Lord Amiens in the first place, which I didn't. The wordplay which ought to provide an alternative route to the answer is decidedly unhelpful as MIEN for "appearance" is not among the synonyms that spring most readily to mind and "first word of his play" is almost useles with its significance only becoming fully apparent in retrospect. It turns out that the work in which the good Lord appears is "As You Like It", and anyone wondering (as I did) whether the first word of a play is quite the same thing as the first word of the title of a play can be reassured that our setter has both angles covered because the first word spoken in "As You Like It" actually is "As".
24
Buzzer made little noise? (4)
WASP - WAS P (made little noise - P, quiet in music)
26
Tank is huge, not small (3)
VAT - VA{s}T (huge) [not small]