I am looking to extend the swash of the character in the attached image. I am a begginer with illustrator (i know enough to get by most times) I only want the line extended and not the rest of the "t".
Glyphs are treated by Illustrator as text so, to extend the line by dragging anchor points, first you need to turn the glyph into a shape so that you have actual anchor points to drag. You can do that by coping the glyph itself into a separate layer, selecting it, then going to Object > Expand. Then, you will have a shape to work with.
Depending on the font there are sometimes alternate characters to choose from as well. These may include "swash" variations. Open "Window>Type>Glyphs" to view them. Double-click a charaacter to add it to an active text block.