If i uninstall Norton Antivirus to install another, will my virus be active again?

a couple of years ago i got some kind of trogan on my laptop, but Norton caught it and Quarintined it ( I didn't know how to set it up to completly remove it). Well to make a long story short, my norton has been expired for 1 year now and I can't open it up anymore because it's expired. I want to download this other antivirus program i bought but it's asking me to fully remove Norton. So my question is, since Norton Quarantined that virus a couple of years back and if I remove Norton (even though its expired) will that virus become active again?