What is the make and model of the sub and the model of the TV?
Just a subwoofer by itself won't get you surround sound. A subwoofer only provides bass.
You won't be able to connect a powered or passive subwoofer directly to the TV.
TV audio outputs are usually fixed volume so the sub level wouldn't change with the TV speaker level.
Many TVs won't let you turn on the audio output without turning off the internal TV speakers so you would only hear the sub and it's volume would be constant.
If the sub isn't self powered it becomes even more expensive and less possible.