Should I tell the truth about my future plans?

When I’m applying for work experience, should I include the fact I already have a training contract or will this put emloyers off from taking me on?

I have a training contract offer and will be starting with my firm later this year. However, I am very keen to gain further legal work experience in a different variety of firms/businesses to enable me to have the best start and confidence when I begin my TC. When I’m applying for work experience, should I include the fact I already have a TC or will this put employers off from taking me on?