The young woman is not introducing a new character into the Song. She is still talking about the young man. She refers to her beloved as a king. Later she will refer to him as a shepherd (Song of Solomon 1:7–8). These are not two different people but two ways of talking about the same young man.1 Referring to him as a king speaks of the high regard she has for him.
Being brought to his chambers implies that she is thinking of their wedding night.2 She is expressing her longing for that special night when their marriage will be consummated.
These opening verses express the young woman’s desires (Song of Solomon 1:2–4), not the actual fulfilment of them. She is anticipating something that hopefully lies in the future. Her desires are wholesome and good, but as the reader we do not know yet if her beloved feels the same way or if she is stirring up these desires at the right time.3
4 Draw me after you; let us run. The king has brought me into his chambers. We will exult and rejoice in you; we will extol your love more than wine; rightly do they love you.