Overdrive is a passive utility program which reduces the cooldowns of other programs by 2 turns down to a minimum of 1 turn, but increases their PWR costs by 1. Program cooldowns of 1 turn (or 0 turns) are not reduced by Overdrive, but their PWR cost is still increased by 1. It has no effect on passive programs, except Emergency Reserve. Overdrive can be bought from some Server Terminals for 700 credits.
Overdrive's effect always applies while it is installed, and cannot be enabled or disabled at will. Overdrive only reduces other programs' cooldowns at the time they are used, so if Overdrive is installed while another program is already on cooldown, it does not reduce that program's cooldown timer. If Overdrive is sold while another program is on cooldown, it also does not increase that program's cooldown timer.
If Overdrive and Charge are both installed, their effects stack, so that other programs' PWR costs are reduced by 1 down to a minimum of 0, and their cooldowns are reduced by 1 turn down to a minimum of 1 turn. However, every active program will have a cooldown of at least 1 turn, even if it would normally have no cooldown.
Overdrive is a bad program, which hurts more often than it helps. For the cost of 700 credits and a program slot, it lets you use programs with longer cooldowns more often, but it is actively harmful to any program with no cooldown or a cooldown of 1 turn, as it increases their PWR costs by 1 with no upside. This includes most breakers.
The main problem with Overdrive is that reducing programs' cooldowns is only worthwhile if you can afford to use them more frequently; but the increased PWR costs make it less likely that you actually can. So Overdrive can only be worthwhile in specific combinations, and generally only works in builds which generate a lot of PWR.
For many programs, Overdrive either has no benefit or makes them strictly worse:
There are a few specific programs which do synergize with Overdrive, all of which are generators:
Other programs with longer cooldowns become different when combined with Overdrive, but whether they are better or worse depends on your loadout and strategy:
Overall, the vast majority of loadouts have at least one program harmed by Overdrive; there is almost always a better program you could install instead of Overdrive. It is very rarely worth 700 credits, and even if you find it for free in a Program Compile side-mission, an empty program slot is usually preferable (though you could install it just long enough to sell it for 350 credits).