You should always make provisions with your band for any overtime playing, just in case your event goes on longer than expected. This should not be a problem for most bands. Also, ask the band to arrive an hour early, so you can take care of any last-minute details.
When hiring a band, be absolutely sure you understand exactly the kind a band they are, and whether they'll be appropriate for your event. It's doubtful that a heavy-metal band will be appropriate for a wedding, and a country band just won't fit a punk party.