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Selection of Speaker of House from Wikipedia

The House elects its speaker at the beginning of a new Congress (i.e. biennially, after a general election) or when a speaker dies, resigns or is removed from the position intra-term. Since 1839, the House has elected speakers by roll call vote.[6] Traditionally, each party's caucus or conference selects a candidate for the speakership from among its senior leaders prior to the roll call. Representatives are not restricted to voting for the candidate nominated by their party, but generally do, as the outcome of the election effectively determines which party has the majority and consequently will organize the House.[7] As the Constitution does not explicitly state that the speaker must be an incumbent member of the House, it is permissible for representatives to vote for someone who is not a member of the House at the time, and non-members have received a few votes in various speaker elections over the past several years.[8] Every person elected speaker, however, has been a member.[7]
Representatives who choose to vote for someone other than their party's nominated candidate usually vote for someone else in their party or vote "present". Anyone who votes for the other party's candidate would [USUALLY, BUT NOT NECESSARILY] face serious consequences, as was the case when Democrat James Traficant voted for Republican Dennis Hastert in 2001 (107th Congress). In response, the Democrats stripped him of his seniority and he lost all of his committee posts.[9]
To be elected speaker, a candidate must receive a majority of the votes cast. If no candidate wins a majority, the roll call is repeated until a speaker is elected.[7] Multiple roll calls have been necessary only 14 times (out of 126 speakership elections) since 1789; and not since 1923 (68th Congress), when a closely divided House needed nine ballots to elect Frederick H. Gillett speaker.[1] Upon winning election the new speaker is immediately sworn in by the dean of the United States House of Representatives, the chamber's longest-serving member.[10][11]

With the small Republican majority, the Democrats could join with the RINO caucus to elect Liz Cheney. They could immediately be rewarded.