Can they still track my cellphone if I replace the cell phone with a new one?

If someone loaded a cell spyware app on my phone, then I replace the phone with a new one, can the person still track my calls and messages on my phone? Someone loaded cell spyware on my previous phone so they were tracking my calls, sms, mms, gps, etc. I got a new phone now for my cell number, so is the person still able track everything on my phone? Is it possible to load spyware remotely?