The Collaborative International Dictionary of English v.0.48:

Clearance \Clear"ance\ (kl[=e]r"ans), n.
   1. The act of clearing; as, to make a thorough clearance.
      [1913 Webster]

   2. A certificate that a ship or vessel has been cleared at
      the customhouse; permission to sail.
      [1913 Webster]

            Every ship was subject to seizure for want of
            stamped clearances.                   --Durke
      [1913 Webster]

   3. Clear or net profit. --Trollope.
      [1913 Webster]

   4. (Mach.) The distance by which one object clears another,
      as the distance between the piston and cylinder head at
      the end of a stroke in a steam engine, or the least
      distance between the point of a cogwheel tooth and the
      bottom of a space between teeth of a wheel with which it
      engages.
      [1913 Webster]

   Clearance space (Steam engine), the space inclosed in one
      end of the cylinder, between the valve or valves and the
      piston, at the beginning of a stroke; waste room. It
      includes the space caused by the piston's clearance and
      the space in ports, passageways, etc. Its volume is often
      expressed as a certain proportion of the volume swept by
      the piston in a single stroke.
      [1913 Webster]

WordNet (r) 3.0 (2006):

clearance
    n 1: the distance by which one thing clears another; the space
         between them
    2: vertical space available to allow easy passage under
       something [syn: headroom, headway, clearance]
    3: permission to proceed; "the plane was given clearance to
       land"

Moby Thesaurus II by Grady Ward, 1.0:

229 Moby Thesaurus words for "clearance":
   Lebensraum, absolution, acquitment, acquittal, acquittance,
   aesthetic distance, air space, allowance, amortization,
   amortizement, ample scope, approval, authority, authorization,
   back country, bill of health, binder, blank check, caesura,
   carte blanche, cash, cash payment, certification, cleaning out,
   clear space, clearing, compass, compurgation, consent, countenance,
   debt service, deep space, defecation, defrayal, defrayment,
   depletion, deportation, deposit, depths of space, desert,
   destigmatization, destigmatizing, detachment, disbursal, discard,
   discharge, discharging cargo, discontinuity, disculpation,
   disjunction, dismissal, disposal, disposition, distance,
   distance between, distant prospect, divergence, doling out,
   double space, down payment, drainage, draining, earnest,
   earnest money, egress, ejection, elbowroom, elimination, em space,
   empowerment, empty view, emptying, en space, enabling, endorsement,
   enfranchisement, entitlement, eradication, evacuation, excretion,
   exculpation, excuse, exhausting, exhaustion, exile, exoneration,
   expatriation, explanation, expulsion, extent, farness, fiat, field,
   forgiveness, free course, free hand, free play, free scope,
   freeboard, full pratique, full scope, full swing, gap, glade,
   headroom, hiatus, hire purchase, hire purchase plan, hole,
   infinity, installment, installment plan, interest payment, interim,
   intermediate space, interruption, interspace, interstice, interval,
   jump, justification, lacuna, latitude, leap, leave, leeway, length,
   light-years, liquidation, living space, long rope,
   maneuvering space, margin, mileage, monthly payments, never-never,
   no holds barred, off-loading, open country, open space, ostracism,
   outback, outlawing, outlawry, pardon, parsecs, pass, passport,
   paying, paying off, paying out, paying up, payment,
   payment in kind, payoff, permission, perspective, piece, plain,
   play, prairie, pratique, prepayment, protection, purgation, purge,
   purging, quarterly payments, quietus, quittance, range,
   ratification, rationalization, reach, regular payments,
   rehabilitation, reinstatement, release, remission, remittance,
   remoteness, removal, restoration, retirement, riddance, room,
   room to spare, rope, safe-conduct, safeguard, sanction,
   satisfaction, scope, sea room, separation, settlement, severance,
   single space, sinking-fund payment, space, space between, span,
   spare room, spot cash, steppe, stretch, stride, suspension, swing,
   terrain, territory, time interval, tolerance, unloading, venting,
   verdict of acquittal, vindication, visa, voidance, voiding,
   warrant, warranty, way, ways, weekly payments, wide berth,
   wide-open spaces, wilderness, withdrawal



Bouvier's Law Dictionary, Revised 6th Ed (1856):

CLEARANCE, com. law. The name of a certificate given by the collector of a
port, in which is stated the master or commander (naming him) of a ship or
vessel named and described, bound for a port, named, and having on board
goods described, has entered and cleared his ship or vessel according to
law.
     2. The Act of Congress of 2d March, 1790, section 93, directs, that the
master of any vessel bound to a foreign place, shall deliver to the
collector of the [dis ot?] from which such vessel shall be about to depart, a

manifest of all the cargo on board, and the value thereof, by him
subscribed, and shall swear or affirm to the truth thereof; whereupon the
collector shall grant a clearance for such vessel and her cargo; but without
specifying the particulars thereof in such clearance, unless required by the
master so to do. And if any vessel bound to any foreign place shall depart
on her voyage to such foreign place, without delivering such a manifest and
obtaining a clearance, the master shall forfeit and pay the sum of five
hundred dollars for every such offence. Provided, anything to the contrary
notwithstanding, the collectors and other officers of the customs shall pay
due regard to the inspection laws of the states in which they respectively
act, in such manner, that no vessel having on board goods liable to
inspection, shall be cleared out, until the master or other person shall
have produced such certificate, that all such goods have been duly
inspected, as the laws of the respective states do or may require, to be
produced to the collector or other officer of the customs. And provided,
that receipts for the payment of all legal fees which shall have accrued on
any vessel, shall, before any clearance is granted, be produced to the
collector or other officer aforesaid.
     3. According to Boulay-Paty, Dr. Com. tome 2, p. 19, the clearance is
imperiously demanded for the safety of the vessel; for if a vessel should be
found without it at  sea, it may be legally taken and brought  into some
port for adjudication, on a charge  of piracy. Vide Ship's papers.