Across

• 1.

  SHIITE: SH(II-T)E
• 4.

  HIGHCLASS: HI-G(H-C)LASS
• 9.

  TAFFRAIL: TAFFRAIL ("fat" rev.)
• 10.

  SUMMAE: SUMM(A)Er
• 11.

  REVVED: RE(V-V)ED
• 12.

  UPPERS: UP(PER)S
• 14.

  ASHHEAP: A-SH-HE-A-P
• 16.

  LIEGES: LIE(G-E)S
• 17.

  INDUCE: INDUCE (anag.)
• 19.

  ERRED: ERRED (pun)
• 22.

  SATCHEL: SATCHEL (anag.)
• 24.

  EXXON: E(X-X)ON
• 25.

  TWIDDLES: TWID(D)LES (anag. + "d")
• 27.

  BRAVER: B-RAVER
• 28.

  SERVE: SE(RV)E
• 30.

  PIAZZA: PI(A)ZZA
• 31.

  PILLAR: P(ILL)AR
• 32.

  ZAQQUM: ZAQQUM (first letters)
• 33.

  DIRECT: DIRE-CT
• 34.

  RESUMED: R(ESUM)ED ("muse" rev.)
• 35.

  GROOMS: G-ROOMS

Down

• 1.

  STRAWWINE: STRAW WINE (anag.)
• 2.

  HAJJES: H(A-JJ)E'S
• 3.

  TREKKED: TRE(KK)ED
• 4.

  HICCUP: HICCUP (anag.)
• 5.

  GARISH: GARISH (pun)
• 6.

  CUDGEL: CUD-GEL
• 7.

  LAYETTES: LAYETTES (anag.)
• 8.

  ABBEYS: AB(BE)YS(s)
• 13.

  ELECTRA: ELECT-RA
• 15.

  ANNUAL: ANNU(AL)
• 18.

  REGGIE: R-EGG-IE
• 20.

  DESERTS: D-ESERTS ("trees" anag.)
• 21.

  AORTAE: A-ORT-A-E
• 22.

  SNAFUS: SN(AF)US ("suns" rev.)
• 23.

  THEISM: THE(IS)M
• 26.

  LEERIER: L-EERIER
• 27.

  BAZAAR: BAZAAR (homophone)
• 28.

  SAYYID: SAY(Y)ID (anag. + "y")
• 29.

  VACUUM: VAC(U)UM