A verbal agreement can also be cancelled, verbally.   And if the committee member was not authorized to do the the bookings, there might not even have been a real verbal agreement in the first place.

A booking, like all contracts, requires a meeting of the minds--both parties have to agree--if your club makes its booking decisions by committee, and the committee didn't agree to offer the booking, but one of the members made an inquiry, then the performer may have mistaken an inquiry for an offer.

In realistic terms, the club always has the upper hand in these situations, and the performer, right or wrong, has not much choice but to go along. The threatened legal action is too costly, in both time and money, to pursue, (though sometimes, if you get somebody mad enough, they'll initiate something)--

My suggestions are(not necessarily in this order):

1) Find out from what happened from the performers point of view.

2)Call the ex-committee member and find out what he/she intended

3) Clarify the situation, to the performer politely, but directly, clearly, and firmly-

4)If there is still an issue, have a lawyer write a letter that states your position(you should have a couple lawyers amongst your club's members and supporters, and, as a habit, you should have an occasional sitdown with them to make sure the way that you and your committee are doing business isn't going to cause any other problems)--

5) Have a long discussion in which it is made clear to everyone on the committee what they can and can't say to people, performers and otherwise-

6)Offer the performer some token, perhaps even a booking at another time, with apologies for the misunderstanding. (This is optional--you don't owe anything, but bad feelings linger, and performers will talk, etc)