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All answers having "Zero" as clue:

3 Character Answers:

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NIL

NOE

ZIP



4 Character Answers:

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COKE

HOUR

INON

LOVE

NADA

NONE

NULL

OVAL

TARE



5 Character Answers:

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AUGHT

BAGEL

NIHIL

OUGHT

RESET

ZILCH



6 Character Answers:

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CIPHER

GATEAU

MOSTEL

NAUGHT

NOTANY

NOTONE

NOUGHT



7 Character Answers:

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CEILING

INTEGER

NOT1BIT

NOTABIT

NOTAONE

NOTHING

WORRIED



8 Character Answers:

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BIGLOSER

GOOSEEGG

NARYAONE

NOTAWHIT



9 Character Answers:

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NONEATALL

TOLERANCE



11 Character Answers:

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ACTORMOSTEL

XAXISORIGIN



15 Character Answers:

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COUNTDOWNENDING

FIGHTERAIRCRAFT