I found this quite an easy puzzle, solving time 14 mins.   I spotted a Nina (i.e. a hidden message) in the grid. In case solvers wish to look again first, I refer to this after the clue explanations.

* = anagram   < = reversed

ACROSS

1 SUS SEX

4 STUBBS   “Stubs”

10 HEALTH INSURANCE    Cryptic definition I got straightaway which helped.

11 MAY OR

12 M U L(a)TITUDE

13 PARSE C

15 EXISTS   Sexist with the first s moved to the end.

16 ST AN CE

18 BU(r)YING

21 I R R IT ATE D

22 LEHAR     Rachel< less c (about)

23 THIN ON THE GROUND     I think this refers to an ad from way back for muscle building (Charles Atlas).  Definition = rare

24 NERVES    (Severn)<  with the er not reversed, I think

25 SHRE(W)D

DOWN

1 S (C HEM) A

2 S (EA(r)LY) HAM TERRIER   r = king

3 (c)ENTER

5 T U R(i)GIDITY

6 BAN QUETING HOUSE    (question huge)*

7 SW (ED) EN   news<

8 FIL(l) MIC

9 IS OLDE(n)

14 SUNSTROK E    (trunks so)*

17 E STATE

18 BAD GER(m)

19 MI(L)T ON

20 E (ROD) ED   Dee<

22 LURCH   Double definition

NINA:   look in sixth and tenth rows

We know the words ‘enunciate’ and ‘announce’ but not many of us may be familiar with
the one at 6d. However, it’s obtainable easily from wordplay. Seasoned solvers will get all
the other Down clues in a ‘read the clue and write the answer’ mode. The Across clues are
also on predictable lines. Altogether, a beginner-friendly puzzle.

Across

1 CLAUSE - c(L)ause - container/contained

4 RECEDE - re, cede - charade

8 RACQUET - “racket” - homophone

9 ESPOUSE - E, spouse - charade

11 AFFIRMABLE - a, f, firm,able - charade

12 NEWT - (went)* - anagram

13 TEETH - te, (the)* - charade with an anagram

14 LISTENER - (linerset)* - anagram

16 CRACKPOT - crack, (top)* - charade with an anagram - For me a ‘crackpot’ is a crazy person. Three dictionaries that I looked up support me; only COD has the meaning “eccentric or foolish person”.

18 PASTE - past, E - charade

20 FAIR - double definition

21 PROTRACTED - (reportatDC)* - anagram

23 ALREADY - Al, ready - charade

24 LIBERAL - double definition

25 NETTLE - (letten)* - anagram

26 RELENT - re, Lent - charade

Down

1 CHAFF - cha, ff. - charade

2 ACQUIRE - “a choir” - homophone

3 STEAMSHIP - steams, hip - charade

5 ENSUE - E, N, Sue - charade

6 ENOUNCE - (-m)en, ounce - charade

7 ELSEWHERE - (heelswhere)* - anagram

10 ABOLITION - (aboilonit)* - anagram

13 TARPAULIN - tar, Paul, in - charade

15 SUPERVISE - super, vi, SE - charade

17 CURRENT - cur, rent - charade

19 SECRETE - SE, Crete - charade

21 PEDAL - (plead)* - anagram

22 EXACT - ex, Act - charade

dd = double definition
cd = cryptic definition
rev = reversed or reversal
ins = insertion
cha = charade
ha = hidden answer
*(fodder) = anagram

Quite an enjoyable and easy puzzle somewhat spoiled by two possible errors (9A & 25D)

Across
1 PIMPLE Ins of MP (military police or redcap) in PILE (stately home; although Chambers has “tall building”)
4 DRESDEN Dres (s) den (retreat) fine decorated china made in Saxony (Royal Saxon porcelain factory established at Meissen, 1710
9 LACERATED Cha of LACE (fabric) RATED (valued)
10 SPLIT Ins of P (pennies or coppers) in SLIT (lance) To split is to chop (definitely not shop) so I reckon there has been a typo
11 DONNE sound like “done” (finished)
12 PORBEAGLE Cha of P (pressure) OR beagle (hound)
13 NITRITE N (knight) I (iodine) trite (hackneyed or common)
15 TOMATO Ins of MAT in TOO
17 SNITCH Ins of NIT in SCH
19 SINE DIE sine (ratio or relationship of opposite over hypotenuse) die (come to an end)  indefinitely adjourned
22 ELEMENTAL *(meet neil a)
24 ON CUE Ins of CU in ONE
26 NAIVE Ins of I (interest) in NAVE, body of the church)
27 INANIMATE *(maintain e)
28 SPECTRE *(respect)
29 BEAT IT be a tit

Down
1 PALADIN Ins of LAD in PAIN
2 MACON MA (Master of Arts, scholar) C (caught) ON (I am on shorts as I do not wish to have to visit the loo every so often)
3 LARCENIST *(Neil’s cart)
4 DIDEROT Formulaic cha Denis Diderot (1713–1784) was a French philosopher and writer.
5 ENSUE ensu (R) e
6 DELIGHTED Ins of light (luminary) in DEED (performance)
7 NETHER ha
8 STAPLE Ins of P (prince) in STALE (flat)
14 TANGERINE Ins of anger (passion) in TIN (can) E (Egyptian)
16 MANDOLINE Man (staff) do line (complete score)
18 HOTLINE *(in hotel)
19 SULTAN sultan (a)
20 EVEREST simple cha for the highest peak on Earth
21 KEYNES Key (leading) NES (rev sen) John Maynard Keynes (1883–1946) was a British economist whose ideas, called Keynesian economics, had a major impact on modern economic and political theory as well as on many governments’ fiscal policies.
23 EVENT E (Ethiopian leader) vent (opening)
25 CHART C (for catch???) Hart (a male deer) I wonder whether this is yet another typo. C in cricket scoring stands for ‘caught’. Chambers does not support extending this abbreviation to ‘catch’