Hi Edward, this is a Tie:
A tie is a gently curved arch connecting the heads of two notes of the same pitch. Ties indicate that the note should be played once and held for the length of the initial note’s value plus the connected note’s value.
Have you seen our write up on: How to Read Tabs, Chord Graphs, and Chart Symbols. This article will help answer any other similar questions about sheet music you may have 🙂