Words and phrases for expressing contrast include:
but, however, although, nevertheless, on the other hand, on the contrary

Contrast is a complex topic – there are different kinds of contrast:

I felt ill. I went to work.
I don’t think that’s a good idea. I think it’s a terrible idea.
The money is good. The conditions are awful.

You cannot use all of the words and phrases for all of the examples.

on the other hand is most commonly used to consider two different sides to an idea or argument. Of the above examples, it can only be used for the last one:

The money is good. On the other hand, the conditions are awful.

Of the original examples:

She does a lot of sport. She's also a keen gardener.. (addition)
I am waiting for your reply. Furthermore, I will consider legal action...(addition)
Regular exercise is essential for a healthy lifestyle. A stress-free lifestyle is also important. (addition)