Look closely to see where the aggressive shoot orginates from. It might be a rootstock sucker. If so, cut it back to the truck. If it is just a watersprout, than I would cut it back to the size of the canopy and it should just send out regular side shoots. Although, some people think you should cut those back to the truck as well.

I think the form of red finger lime is to grow rynaway shoots. I don’t like them and cut them off at a fork, hoping to promote a fuller canopy. I have no idea if it will happen. But I do it that way ‘cause I don’t like them.

Thanks for your reply, here's a close up of the shoot where you can see it stemming from the trunk but it's not the lowest branch and it's above the graft so I'm not sure, on the other hand despite the leaves resembling those on the other branches they are bigger in size.

I've already had to cut rootstock from the trunk of a kaffir lime but that was easy to spot as the leaves were completely different.

Thanks for all your replies,

Nikthegreek, what do you mean when you say prune it back to an eye?

This shoot is a single stem with no forks.

That is definitely a waterspout - I've read a lot that says you should prune them off completely because they sap energy and nutrition from the rest of the tree. Personally, if it was my tree, I would cut it back to the size of the rest of the canopy and then watch it. If it begins to behave like a normal branch, then you're done. If it continues to grow vigorously, then chop it off.

Thanks for all your replies, I think I'm going to just chop it off at the trunk and be done with it, it will have plenty of time to grow new branches.

Prune to an eye means cut just above the point where a leaf grows (or may grow).