Natural gas is notoriously the least CO2-emitting fuel among fossil fuels. For this reason, in the medium run it will likely drive the transition phase of the decarbonization of the energy system. It is more difficult to make a forecast for the long run, instead: models in fact show conflicting results because if it is true that ambitious mitigation targets will imply a full decarbonization of the economy, there is huge uncertainty concerning the actual development of carbon-free or negative-emissions technologies (starting from CCS) which might allow the continuous use of fossil fuels. This is in addition to the difficulties related to the actual decarbonization of some sectors, especially in industry and transport.
In any case, things seem bright for natural gas in the short term: this is what emerges from a specific study released by the International Energy Agency (IEA): in this post I link to the relevant webpage which discusses all the details and where the full report can be downloaded.