You should NEVER EVER reuse old TIM (thermal interface materials) after it has cured. So once you broke the cured bond, the plan should have been that you were going to apply a fresh new layer of TIM. And obviously, that means you should have had fresh TIM on hand before removing the heatsink.
But of course, hindsight is 20/20.
That said, there is no need to worry about a "shortage". Remember, TIM is designed to "conduct" heat - so you want a "short" in that sense. If you meant some sort of electrical short, no current flows between the CPU and heatsink so there's no worries there either. In fact, the best transfer of heat occurs with direct metal to metal contact. The TIM is only there to fill in the microscopic pits and valleys in the mating surfaces, pushing out any insulating air.
The only time you need to be concerned with electrical shorts and TIM is if you are messy and/or use too much TIM and it gets on the electrical contacts of the CPU, the socket, or the motherboard. But note even then, and contrary to what many believe, most TIMs do NOT conduct, or cause capacitance issues. The DC voltages are just too low in potentials and as such, will continue through their intended circuits as designed. Even with silver based TIMs!
Now about the TIM being dry. That's no big deal either. It is important to note the only reason TIM comes in a semi-liquid form is so you can squeeze it out of the tube and spread it evenly across the die. Even if the TIM totally dries out, the solids that remain are still occupying those microscopic pits and valleys, preventing any insulating air from getting inside.
See
The Heatsink Guide.
And lastly TIM
never needs to be replaced just because X amount of time has passed. TIM will easily last 10, 15 years or even longer AS LONG AS the cured bond between the processor and heatsink is not broken. If someone tells you you need to replace your TIM because X number of months or years have passed, they were misinformed and are now giving you bad advice. The risk of damaging a pin, pad, or zapping the CPU with ESD through accident or mishandling is too great.
There is not one single TIM maker, CPU or GPU maker, cooler maker, motherboard maker, or computer maker who claims or recommends TIM be replaced on any scheduled or periodic basis. Not one!
It is true over several years, older TIM may lose a couple (typically less than 5°C - more like 2 - 3°) degrees in efficiency. But it is important to note if your system "
needs" those 2 - 5° to keep from hitting excessive over-temp thresholds, you have greater problems than old TIM - like inadequate case cooling, too extreme overclocking, or a failing CPU fan.
While proper cooling is essential, cooler does not automatically mean better. As long as your heat sensitive device is maintained comfortably within its "normal operating temperature range" that's just fine. A CPU running at 30°C will
NOT be more stable, perform better, or have a longer life expectancy than a CPU running at 55°C.
So again, the only time you need to replace TIM is if the cured bond is broken. Then the mating surfaces should be thoroughly cleaned of old TIM, and a fresh, as thin as possible, new layer of TIM should be carefully applied.