In general, when you have a solder pad with no electrical connection, then it's simply there as a physical anchor. If the component is otherwise secure, you can leave it off.

However, a transistor is not going to work if one of the three legs is not connected to something electrically, so I doubt there's no connection here. Is there an electrical connection on the other side of the board for this particular leg?

No! What? Why? You cannot just change an electrical circuit around willy nilly.

Look at your schematic so you know how/where this leg is supposed to be connected. Transistors have three legs and all three legs are electrically connected to something.

Post some photos of what you're talking about and the relevant part of the schematic.

Sounds like the pad was supposed to connect to something after all. Show us some photos, then maybe we can see the problem.