John Gill Commentary 1 Kings 1:20

"And thou, my lord the king, the eyes of all Israel are upon thee, that thou shouldest tell them who shall sit on the throne of my lord the king after him." — 1 Kings 1:20 (ASV)

And you, my lord, O king
As for you, or what concerns you, or is incumbent on you, will appear from the expectations of the people:

the eyes of all Israel [are] upon you, that you should tell them
who shall sit on the throne of my lord the king after him ;
this she said, to dissipate any fears that might possess his mind on hearing what Adonijah had done, that the people in general had assented to it, and encouraged him to it; whereas the body of the people were waiting to hear what was the will and determination of David: for they not only considered him as having a power to name a successor, as was afterwards done by Rehoboam, but as one that had the mind of God revealed to him who should be his successor, to which they should pay a regard.