+1 to Bill.
You'd be able to keep your rear derailleur. But you'd need new shifters (expensive! - or at least a new right shifter), chain, cassette - - and for optimal performance, perhaps new chain rings. It's possible you'd need a new rear wheel (it depends).
Not a cheap conversion for just one more gear... I converted a 7-speed to 9, but that was mainly because I wanted STI levers, which a rather bigger difference.