Complete
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1 8 11 14 18 20 22 2 19 17 10 3 9 4 16 15 5 21 23 6 12 7 13
  1. 1a Multinational computer company, founded as PC's Limited in Texas in 1984 (4)
  2. 3a Mocking — scornful (8)
  3. 8a Long skirt ending below the calf (4)
  4. 9a Pet animal (informal) (8)
  5. 11a Small North American rabbit — not coal tit (anag) (10)
  6. 14a Inappropriate lack of seriousness (6)
  7. 15a Gripping tool (6)
  8. 17a Cabby (4,6)
  9. 20a Raise objections (8)
  10. 21a Princess Royal (4)
  11. 22a Fly away (4,4)
  12. 23a Cricketing extras (4)
  13. 1d Abode (8)
  14. 2d It keeps things moving — a live tax (anag) (8)
  15. 4d Sharpness (6)
  16. 5d Source of spirits (10)
  17. 6d Cop shop (informal) (4)
  18. 7d Belt-tightening measures (4)
  19. 10d Temporary traffic management scheme (10)
  20. 12d Wonderful (8)
  21. 13d Those wrongfully replacing incumbents (8)
  22. 16d Venetian painter — shade of red (6)
  23. 18d Person from Paisley, say (4)
  24. 19d Totally out of control (4)