Why was Mary Queen of Scots not a threat to Elizabeth 1?

Answer 1

This really depends on point of view.

Yes:

She was a potiental heir to the English throne and, as a Catholic, was an iconic figure to the Catholic population of England. They wanted her on the throne so that they would have a monarch who shared their religion for various political reasons. She did sign a document to say she wanted a certain plot on Queen Elizabeth's life carried out and that she supported it.

No:

However, at this point she had been locked up for 18/19 years and never been let out by the very same woman. Even though it would get her the freedom she desired she automatically regretted that she signed that sheet. She needn't worry though. Her secret mail had been known about from day one. It had been organised by her captors to see if they could find out anything incriminating. So she was beheaded for 'treason'.

Answer 2

Honestly? Because Mary was forced into exile in a place where being a threat wasn't exactly a possibility. Moreover, Elizabeth simply had significantly more manpower, political power and general backing than Mary so the threat was brought down to a minimum.