On 22nd July (the last time the party's GC was able to meet), it passed without dissent an emergency motion of no confidence in the London Labour Party's conduct of the shortlisting process. (leftfutures.org)
At its most basic, «a confidence and supply» deal guarantees a minority government the support of another party when the House votes on motions of no confidence (and, before the Fixed - Term Parliaments Act, on supply bills, where a loss would also have effectively terminated the government's mandate). (politics.stackexchange.com)
Traditionally, votes on the Queen's Speech are regarded as motions of confidence. (channel4.com)