We need a secondary source on that claim. A 2024 construction start is not in line with what City Staff have indicated before, nor does it make sense given how advanced planning for the Relief Line Short is.
The Environmental Assessment for the project will be complete in late 2017/early 2018. After that point, the TTC can either complete 30% design work, and enter into a design/build agreement with an outside firm to complete the line, OR TTC can complete 100% design while concurrently constructing the line. In either case, it won't take six to seven years to design the Relief Line; the design phase typically lasts only one or two years before construction start. Furthermore, a delay of 6 to 7 years will dramatically increase the price of the project. So what are they planning to be doing during that delay?
Perhaps Paula Fletcher was talking about the Relief Line northern extension when she made that comment. The earliest that extension could begin construction is 2024, if it follows a similar planning timeline as the Relief Line Short (four years from planning start to EA completion + two years design).