1) Asserter 2) Asserter of a right or title 3) Claimant 4) Horse for sale before a race 5) One asserting something 6) One staking out 7) Person making an assertion 8) Prospector, at times 9) Seeker of rights 
• (n.) One who claims; a claimant.
Claim'er noun One who claims; a claimant. 
Race where a horse is handicapped by its trainer, with the weight relating to the amount of money the horse would cost should someone claim it afterwards.
a person who makes a claim; claimant. · · a horse participating in a claiming race. · Seeclaiming race.