Old growth forests aren't carbon sinks, modulo some slight metabolic shifts as CO2 increases. Forests tend to reach equilibrium between carbon consumption (e.g. autotrophic photosynthesis) and carbon emissions (e.g. fire, erosion of organic material into marine ecosystems, and heterotrophic activity such as grazing and decomposition).[1]
Forests are currently a carbon sink primarily because of centuries of harvesting, and because of increases in atmospheric CO2 improving autotrophic efficiency. As they grow back and grow faster they're absorbing more carbon than they release, but this is temporary. Eventually there won't be more space to grow, and metabolic efficiencies will diminish and possibly even flip--e.g. higher temperatures can increase decomposition rates. Reforestation can't fix the problem, only buy us a little time.
But don't take my word for it:
> Although land practices have the potential to offset a small but significant portion of anthropogenic emissions, they should ultimately be seen (with the exception of geological sequestration through BECCS) as a short-term stopgap measure.
Source: The Terrestrial Carbon Sink, Annu. Rev. Environ. Resour. 2018. 43:219–43, https://harvardforest1.fas.harvard.edu/sites/harvardforest.f...
That said, preventing further deforestation is a no-brainer. The annual net carbon flux of a forest is nothing compared to the carbon stored in the tree stands and the soil, much of which is quickly released when the land is cleared.
[1] Heterotrophs are far more efficient today than they were hundreds of millions of years ago.