Across

• 1.

  YEAGER: Y-E-AGER
• 5.

  TARPAULIN: TAR(PAULI)N
• 11.

  TRENT: T(R)ENT
• 12.

  SAILBOAT: S(AIL-BOA)T
• 13.

  VICARIOUSLY: V(IC)ARIOUSLY
• 14.

  PROVISOS: PRO(VI)-SOS
• 15.

  ROWAN: ROW-AN
• 18.

  ENDOWING: END-OWING
• 19.

  SHIVERED: S-HIVE-RED
• 20.

  NATAL: NATAL (double def.)
• 24.

  OBESE: OBESE (hidden)
• 26.

  LEAFIEST: LEAFIEST (anag.)
• 29.

  LEATHERS: LEA(THE)R'S
• 31.

  GLOAT: G(L-O)AT
• 33.

  SELFSAME: SE(L-F)SAME
• 35.

  NORTHEASTER: NORTHE-ASTER ("hornet" anag.)
• 36.

  UNBELIEF: UN(BELIE)F ("fun" anag.)
• 37.

  TREEN: TREEN (anag.)
• 38.

  OTOSCOPES: O-TOS(COP)ES
• 39.

  NINETY: N(I-NET)Y

Down

• 1.

  REBIRTH: R(EBIRT)H (rev.)
• 2.

  NARCOTIC: N(ARC)O-TIC ("car" anag.)
• 3.

  HENRI: HENRI (anag.)
• 4.

  ARTIST: ARTIST (hidden)
• 5.

  VAMOOSE: V-A-MOOSE
• 6.

  EPISODIC: EP(I-SOD)IC
• 7.

  GALLEON: GA(L)LE-ON
• 8.

  SLOW-WITTED: SLO(WWI)TTED
• 9.

  TIARA: T(I)ARA
• 10.

  ENTANGLE: ENT-ANGLE ("ten" anag.)
• 16.

  DEVASTATES: DEVA-STATES
• 17.

  IRENE: I-RENE
• 18.

  UNDIES: UNDIES (pun)
• 20.

  OASIS: O-AS-IS
• 21.

  LIBELANT: LIBELANT (anag.)
• 22.

  OVERSTEP: O(VERST)-EP
• 23.

  EASEMENT: EASEMENT ("tease men" with "t" shifted)
• 25.

  CHEERIO: CHE(E)RIO (anag. + "e")
• 27.

  TABLETS: TAB-LETS
• 28.

  UTTERLY: UTTERL-Y (anag. + "y")
• 30.

  SAFARI: S(A-FAR)I
• 32.

  YOBBO: YO-BB-O
• 34.

  ESSEN: ESSE-N