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up vote 8 down vote favorite

Yo dawg, I heard you like cryptic clues ...

Solve these cryptic clues to reveal (and solve) the final clue.

  1. Well-built steam ship heads East with subtlety (7)
  2. Cost catches new net tournament (7)
  3. Begins amidst messy trash twist (6, 4)
  4. "[Green light objectives incomplete, chief (2, 5)]?"

(5)

To clarify: The quotes and question mark are for the final clue. Clue 4 is completely contained within the square brackets, which are not part of the final clue.

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up vote 8 down vote accepted 
Well-built steam ship heads East with subtlety (7)

FINESSE   (Well-built [FINE] steam ship heads [SS] East [E]; subtlety [def.]) 

Cost catches new net tournament (7)

CONTEST   from @Will

Begins amidst messy trash twist (6, 4)

STARTS WITH   from @Beastly Gerbil 

Green light objectives incomplete, chief (2, 5)

GO AHEAD   (Green light [def.]; objectives incomplete [GOA(ls)] + chief [HEAD])

Meta

Finesse contest starts with "Go ahead?" (5)
GRACE   (G(o) + RACE)     (from @Will in TSL)

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up vote 4 down vote

3 is

Starts with

Because

Messy trash twist indicates an anagram of 'trash twist' which is 'starts with'. Begins amidst is the def

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up vote 3 down vote

Partial answer

Cost catches new net tournament (7)

CO(NTE*)ST

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