From Rietstap, Johannes Baptist (1861). "Armorial général, contenant la description des armoiries des familles nobles et patriciennes de l'Europe: précédé d'un dictionnaire des termes du blason", G.B. van Goor., shows a croissant (mullet) the heraldic mark of the 2nd son, which the 1st earl of Carnarvon was:

"Herbert Comte de Carnarvon - Angleterre - (Lord Porchester, 17 oct. 1780; comte de C., 3 juillet 1793) - Parti d'azur et de gueules à trois lions d'argent armés et lampassés d'or 2 et 1 et un croissant d'argent en chef brochant sur le parti Cimier un dragon ailé de sinople tenant entre ses dents une main senestre de gueules Supports à dextre une panthère d'argent tachetée d'émaux divers la tête posée de front jetant des flammes par la bouche et les oreilles colletée d'une couronne partie de gueules et d'azur et enchaînée d'azur à senestre un lion d'argent colleté d'une couronne de gueules Devise UNG JE SERVIRAY."

English: Herbert, Earl of Canarvon -- England -- (Lord Porchester, 17 Oct. 1780; earl of C., 3 July 1793) - Per pale Azure and Gules three Lions rampant Argent and a crescent argent in the chief between the partitions; Crest: A Coronet of an Earl, On a wreath Argent and Gules a Wyvern with wings elevated Vert holding in the mouth a Sinister Hand couped at the wrist Gules; Supporters: Dexter, a Panther guardant Argent semée of Torteaux and Hurts flames issuant from the mouth and ears proper, and Sinister, a Lion Argent, each ducally gorged per pale Azure and Gules and chained Or and charged on the shoulder with an Ermine Spot Sable; Motto: UNG JE SERVIRRAY (ONE I WILL SERVE)."

However, from Burke's (1878) "Genealogical and Heraldic History of the Peerage, Baronetage, and Knightage", vol 40, shows no crescent (mullet)

"Per pale Azure and Gules three Lions rampant Argent; Crest: A Coronet of an Earl, On a wreath Argent and Gules a Wyvern with wings elevated Vert holding in the mouth a Sinister Hand couped at the wrist Gules; Supporters: Dexter, a Panther guardant Argent semée of Torteaux and Hurts flames issuant from the mouth and ears proper, and Sinister, a Lion Argent, each ducally gorged per pale Azure and Gules and chained Or and charged on the shoulder with an Ermine Spot Sable; Motto: UNG JE SERVIRRAY (ONE I WILL SERVE)."

Given this inconsistency, its probably best to take the coat of arms from the earl's seat, Highclere Castle, itself. The pediment over the from door (picture shown below) shows, although its not in the best shape, definitely shows the croissant/mullet on the coat of arms, although in the center of the shield (we'll put that down to artistic license). Given that the croissant/mullet is repeated on the interior of the castle, it would seem prudent to go with the croissant/mullet on the coat of arms.