Webster's New Collegiate Dictionary gives several definitions for "clap" as a transitive verb, one of which is "applaud". I have never heard it used this way, so I can't recommend it.
I've never heard "clap" used that way, either. The Oxford English Dictionary(OED) gives a similar definition. Interestingly, it uses the term "elliptically" after "transitive":
5c.transitive (elliptically) To clap the hands at, or in honour of, applaud (a person, performance, etc.) with claps. (Rarely, to drive away, out, etc. by clapping the hands.)
a1575 N. HarpsfieldTreat. Divorce Henry VIII (1878) (modernized text) 121 The which John Bacon was whistled and clapped out of Rome.
a1616 ShakespeareJulius Caesar (1623) i. ii. 258 If the tag-ragge people did not clap him, and hisse him, according as he pleas'd, and displeas'd them.
1669 S. PepysDiary 2 Feb. (1976) IX. 436 Endeed, it was very finely sung, so as to make the whole house clap her.
1721 L. Eusden in J. Addison Wks. I. 264 Crowds the sentiments of every line Impartial clap'd.
1820 R. SoutheyLife of Wesley II. 488 A few bucks clapped and encored him.
Notice that the most recent example is from 1820. I think that most native speakers today, at least in the United States, would naturally assume that "clap her" must mean something other than "applaud." If I heard "The audience clapped her," my response might be: "I hope they didn't injure her."
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