Unless you’re very experienced you are unlikely to solve a Mephisto without using Chambers. The idea is that you use the precise wordplay to derive an answer that you then verify in the dictionary. 24A is a perfect example.
Very interesting grid for a puzzle of average difficulty
In the clues, definitions are underlined. Wordplay explanation is followed by very helpful comments.
ACROSS
1 Sussex town greets amateur (8)
HAILSHAM: HAILS-HAM; small town in the Wealden district of East Sussex
6 Request for silence from one following leader of Trappists (4)
TACE: T(rapist)-ACE;
9 Column about part of the book accepted (4)
ANTA: A-NT-A; NT=New Testament;
10 Maori staff nurse joins hospital, cheers all round (6)
TAIAHA: T(AIA-H)A; AIA=ayah=nurse;
12 Guard going around my city (8)
FLORENCE: F(LOR)ENCE;
13 Hot press steel? Yes, but not seriously (12, two words)
TOASTING,IRON: steel=sword; facetious term for a sword;
14 One’s leaving French city borders (5)
ORLES: ORLE(an)S;
17 What you need here is the removal of doubt (8)
SOLUTION: two definitions
18 Inter due to be playing together again (8)
REUNITED: (inter due)*;
22 Mining Engineer set upon relating to life with some moisture (5)
MESIC: ME-SIC;
23 Ecologist pal terribly concerned with crop damage (12)
PESTOLOGICAL: (ecologist pal)*;
24 As before, admit one term in examination that’s stiff (8)
INCORPSE: I-(examination)N-CORPSE;
25 Wrinkly’s game by the way (6)
RUGATE: RU-GATE;
26 Sounds like Welsh person clamours (4)
HUES: sounds like “Hughes”
27 Which ruler’s male, always? (4)
MEER: M-EER;
28 Mostly inside info in sack is for outsiders (8)
OUSTITIS: OUS(TI-p)T-IS;
DOWN
1 Bending on touch, papa with young child interrupts odd aphorism (12)
HAPTOTROPISM: (aphorism)* surrounds P-TOT;
2 Withdraw wine from the south that’s totally finished (8, three words)
IT’S,ALL,UP: PULL-ASTI reversed;
3 Misses Berks after introduction to Lancs (6)
LASSES: L(ancs)-ASSES;
4 One on test in robust court (8)
HALIMOTE: HAL(I-MOT)E;
5 Bank’s spread perhaps (5)
MARGE: two definitions
6 The Duke’s beginning to drop off, I believe (6)
THEIST: THE-(f)IST; duke=fist;
7 Very bad about time in prison cell, alongside huge guy unclothed (10)
CACOTOPIAN: CA-CO(T)OP-(g)IAN(t);
8 Paper girl embraces college in this? (12, two words)
EVENING,CLASS: EVENING-C-LASS; EVENING=evening newspaper; C=college;
11 Heroin’s seen wrongly to show natural wisdom (10, two words)
HORSE,SENSE: HORSE’S-(seen)*; HORSE=heroin;
15 Smart fellow wanting power, announces plants for alcohol additives (8)
ALECOSTS: ALEC-(p)OSTS;
16 Prospective flyer exposes cost at Orly (8, two words)
AIR,SCOUT: AIRS-COUT; French for cost=COUT;
19 Well-known Scot still in with runs for team at first (6)
NOTOUR: still in=NOT OUT then change final T to R;
20 See yours truly with poet take away business card (6)
MEISHI: ME-(r)ISHI: take=R; reference poet Rishi Patialvi 1917-99;
21 Do without cast, mostly old (5)
FORGO: FORG(e)-O;
spelling is US; ODE has only sick2, where New Oxford Am. Dict. gives sick as a variant of sic2.
I got quite stuck at the end of this one and the last two – MEISHI and OUSTITIS – took a few looks.