If it goes well, I'll introduce you to a TV drama series.
Literal
Well went [conditional-たら] serialized-drama [obj-を] introduce [favor-てあげる].
連ドラ is an abbreviation of 連続ドラマ 'serialized drama / TV drama series.' ~てあげる is the benefactive auxiliary — 'do X as a favor for you.' うまくいったら 'if it goes well' is a set conditional. The sentence is casual and slightly condescending (あげる implies doing a favor downward).