Depends on if you control an area of your youth team or not.
If you do control an area under responsibilities, such as training or squad selection, the only way I know to fix it is to temporarily delegate all youth responsibilities. Once you do that, go to the development center, then the overview screen for your youth squad, and you will see the primary tactic dropdown box. Select that to whatever tactic you want them to run.
Note: After writing this I realize that I may have misunderstood your question. I typically use slots 1 and 2 for my main team and slot 3 for my youth. The only way to have 3 completely new tactic slots is to fire the youth manager and take over yourself, which can be irritating for a few reasons.