Meets a need/serves a purpose.
The bill in this context is a theatrical poster/leaflet describing the acts to be presented. If the bill had too few acts, more acts would be sought to 'fill the bill'. This expression appears to have originated in the USA in the 19th Century. It can also sometimes be used when a particular act or event dominates the show.
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The good writer, the great writer, has what I have called the three S's: The power to see, to sense, and to say. ...
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