What does 1x Tacet
mean?
Does it mean "play the following in 1st round only"?
"Tacet" is a Latin musical term meaning (literally) "it is silent". in this case, the number preceding it identifies which repetitions it is to be silent for. Here, the first time through is to be silent. The second time through, do play that segment.
In jazz and other more 'modern' genres, tacet is often used for very short breaks (such as one or two bars). In classical and orchestral music, it is usually reserved for longer breaks (such as entire movements).